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COTANGENT COMPLEX

  • Cotangent complex
  • Construct in algebraic geometry

    In mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric

    Cotangent complex

    Cotangent_complex

  • Kodaira–Spencer map
  • Mathematical object

    {\text{Ext}}^{1}(\mathbf {L} _{X_{0}/k},{\mathcal {O}}_{X_{0}})} . Cotangent complex Schlessinger's theorem characteristic linear system of an algebraic

    Kodaira–Spencer map

    Kodaira–Spencer_map

  • Derived scheme
  • homotopy equivalence in a suitable model category. The (relative) cotangent complex of an ( A ∙ , d ) {\displaystyle (A_{\bullet },d)} -differential graded

    Derived scheme

    Derived_scheme

  • Cotangent bundle
  • Vector bundle of cotangent spaces at every point in a manifold

    especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold

    Cotangent bundle

    Cotangent_bundle

  • Exalcomm
  • from the ring morphism. Deformation theory Cotangent complex Picard stack Illusie, Luc. Complexe Cotangent et Deformations I. pp. 151–168. Tangent Spaces

    Exalcomm

    Exalcomm

  • Luc Illusie
  • French mathematician

    work concerns the theory of the cotangent complex and deformations, crystalline cohomology and the De Rham–Witt complex, and logarithmic geometry. In 2012

    Luc Illusie

    Luc Illusie

    Luc_Illusie

  • Trigonometric functions
  • Functions of an angle

    Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less commonly used. Each of these six trigonometric

    Trigonometric functions

    Trigonometric functions

    Trigonometric_functions

  • Cotangent sheaf
  • In algebraic geometry, given a morphism f: X → S of schemes, the cotangent sheaf on X is the sheaf of O X {\displaystyle {\mathcal {O}}_{X}} -modules

    Cotangent sheaf

    Cotangent_sheaf

  • André–Quillen cohomology
  • Theory of cohomology for commutative rings

    cohomology for commutative rings which is closely related to the cotangent complex. The first three cohomology groups were introduced by Stephen Lichtenbaum

    André–Quillen cohomology

    André–Quillen_cohomology

  • Alexander Grothendieck
  • French mathematician (1928–2014)

    Hakim [fr] (relative schemes and classifying topos), Luc Illusie (cotangent complex), Michel Raynaud, Michèle Raynaud, Jean-Louis Verdier (co-founder

    Alexander Grothendieck

    Alexander Grothendieck

    Alexander_Grothendieck

  • Hyperbolic functions
  • Hyperbolic analogues of trigonometric functions

    derived: hyperbolic tangent "tanh" (/ˈtæŋ, ˈtæntʃ, ˈθæn/), hyperbolic cotangent "coth" (/ˈkɒθ, ˈkoʊθ/), hyperbolic secant "sech" (/ˈsɛtʃ, ˈʃɛk/), hyperbolic

    Hyperbolic functions

    Hyperbolic functions

    Hyperbolic_functions

  • Hochschild homology
  • Theory for associative algebras over rings

    using a self-intersection from the diagonal, or more generally, the cotangent complex L X / S ∙ {\displaystyle \mathbf {L} _{X/S}^{\bullet }} since this

    Hochschild homology

    Hochschild_homology

  • Yoneda product
  • Pairing in algebra between ext groups of modules

    and L X / Y {\displaystyle \mathbf {L} _{X/Y}} corresponds to the cotangent complex. Ext functor Derived category Deformation theory Kodaira–Spencer map

    Yoneda product

    Yoneda_product

  • Derived tensor product
  • _{R}=\Omega _{Q(R)}^{1}\otimes _{Q(R)}^{L}R} is an R-module called the cotangent complex of R. It is functorial in R: each R → S gives rise to L R → L S {\displaystyle

    Derived tensor product

    Derived_tensor_product

  • Perfect obstruction theory
  • {\textbf {L}}_{X}} , where L X {\displaystyle {\textbf {L}}_{X}} is the cotangent complex of X, that induces an isomorphism on h 0 {\displaystyle h^{0}} and

    Perfect obstruction theory

    Perfect_obstruction_theory

  • Almost complex manifold
  • Smooth manifold

    complexified tangent and cotangent bundles. In both cases one demands that the direct sum of the subbundle and its complex conjugate yield the original

    Almost complex manifold

    Almost_complex_manifold

  • Kähler differential
  • Differential form in commutative algebra

    cotangent sheaf can be computed from the sheafification of the cotangent module on the underlying graded algebra. For example, consider the complex curve

    Kähler differential

    Kähler_differential

  • Deformation (mathematics)
  • Branch of mathematics

    Exalcomm Cotangent complex Gromov–Witten invariant Moduli of algebraic curves Degeneration (algebraic geometry) Palamodov (1990). "Deformations of Complex Spaces"

    Deformation (mathematics)

    Deformation_(mathematics)

  • Inverse trigonometric functions
  • Inverse functions of sin, cos, tan, etc.

    domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from

    Inverse trigonometric functions

    Inverse trigonometric functions

    Inverse_trigonometric_functions

  • Derived algebraic geometry
  • Branch of mathematics

    (or motivic homotopy theory) of singular algebraic varieties and cotangent complexes in deformation theory (cf. J. Francis), among the other applications

    Derived algebraic geometry

    Derived_algebraic_geometry

  • Sine and cosine
  • Fundamental trigonometric functions

    the ratio of the hypotenuse length to that of the adjacent side. The cotangent function is the ratio between the adjacent and opposite sides, a reciprocal

    Sine and cosine

    Sine and cosine

    Sine_and_cosine

  • Pierre Cartier (mathematician)
  • French mathematician (1932–2024)

    Discrete Groups and Renormalization. Springer. ISBN 9783540303084. Cotangent complex Dieudonné module MacMahon's master theorem "Pierre Cartier". Institute

    Pierre Cartier (mathematician)

    Pierre Cartier (mathematician)

    Pierre_Cartier_(mathematician)

  • Fibred category
  • Concept in category theory

    in groupoids. One notable example of this is in the study of the cotangent complex for local-complete intersections and in the study of exalcomm. Grothendieck

    Fibred category

    Fibred_category

  • Unit circle
  • Circle with radius of one

    fact, all six standard trigonometric functions – sine, cosine, tangent, cotangent, secant, and cosecant, as well as archaic functions like versine and exsecant –

    Unit circle

    Unit circle

    Unit_circle

  • Symplectic manifold
  • Type of manifold in differential geometry

    abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds. For example, in the Hamiltonian formulation of classical

    Symplectic manifold

    Symplectic_manifold

  • Gromov–Witten invariant
  • Concept in string theory

    genus g is the generating function of the genus g GW invariants. Cotangent complex – for deformation theory Schubert calculus Hori, Kentaro (2003). Mirror

    Gromov–Witten invariant

    Gromov–Witten_invariant

  • Generalized complex structure
  • Property of a differential manifold that includes complex structures

    vector field on M. The cotangent bundle of M, denoted T*, is the vector bundle over M whose sections are one-forms on M. In complex geometry one considers

    Generalized complex structure

    Generalized_complex_structure

  • Holomorphic tangent bundle
  • complex-valued one-forms d z j {\displaystyle dz^{j}} and d z ¯ j {\displaystyle d{\bar {z}}^{j}} provide the splitting of the complexified cotangent

    Holomorphic tangent bundle

    Holomorphic_tangent_bundle

  • Normal cone (algebraic geometry)
  • Scheme in algebraic geometry

    {\displaystyle k} . If L X {\displaystyle {\textbf {L}}_{X}} denotes the cotangent complex of X relative to k {\displaystyle k} , then the intrinsic normal bundle

    Normal cone (algebraic geometry)

    Normal_cone_(algebraic_geometry)

  • Homotopical algebra
  • Branch of mathematics

    full Bloch–Kato conjecture. Derived algebraic geometry Derivator Cotangent complex - one of the first objects discovered using homotopical algebra L∞

    Homotopical algebra

    Homotopical_algebra

  • Cartier isomorphism
  • graded of the conjugate filtration) and the exterior powers of the cotangent complex. Pierre Deligne; Luc Illusie (1987). "Relèvements modulo p2 et décomposition

    Cartier isomorphism

    Cartier_isomorphism

  • Nearby Lagrangian conjecture
  • mathematics Prove or disprove: Any closed exact Lagrangian submanifold of the cotangent bundle of a closed manifold is Hamiltonian isotopic to the zero section

    Nearby Lagrangian conjecture

    Nearby_Lagrangian_conjecture

  • Mirror symmetry conjecture
  • Mathematical conjecture

    Hodge structures. Further, these integrals are actually computable. Cotangent complex Homotopy associative algebra Kuranishi structure Mirror symmetry (string

    Mirror symmetry conjecture

    Mirror_symmetry_conjecture

  • List of trigonometric identities
  • This last expression can be computed directly using the formula for the cotangent of a sum of angles whose tangents are t1, ..., tn−1 and its value will

    List of trigonometric identities

    List of trigonometric identities

    List_of_trigonometric_identities

  • Differentiable manifold
  • Manifold upon which it is possible to perform calculus

    The cotangent space at a point is the dual of the tangent space at that point and the elements are referred to as cotangent vectors; the cotangent bundle

    Differentiable manifold

    Differentiable manifold

    Differentiable_manifold

  • Glossary of real and complex analysis
  • microfunction microlocal The notion microlocal refers to a consideration on the cotangent bundle to a space as opposed to that on the space itself. Explicitly,

    Glossary of real and complex analysis

    Glossary_of_real_and_complex_analysis

  • Regular embedding
  • Y} is a any local complete intersection morphism of schemes, its cotangent complex L X / Y {\displaystyle L_{X/Y}} is perfect of Tor-amplitude [-1,0]

    Regular embedding

    Regular_embedding

  • Ringed topos
  • Topos-theoretic version of a ringed space

    has applications to deformation theory in algebraic geometry (cf. cotangent complex) and the mathematical foundation of quantum mechanics. In the latter

    Ringed topos

    Ringed_topos

  • Inverse hyperbolic functions
  • Mathematical functions

    hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent. They are commonly denoted by the symbols for the hyperbolic functions

    Inverse hyperbolic functions

    Inverse hyperbolic functions

    Inverse_hyperbolic_functions

  • Elliptic complex
  • Here π is the projection of the cotangent bundle T*M to M, and π* is the pullback of a vector bundle. Chain complex Atiyah, M. F.; Singer, I. M. (1968)

    Elliptic complex

    Elliptic_complex

  • Abelian 2-group
  • example is the cotangent complex for a local complete intersection scheme X {\displaystyle X} which is given by the two-term complex L X ∙ = i ∗ I /

    Abelian 2-group

    Abelian_2-group

  • Vector space
  • Algebraic structure in linear algebra

    O. The cotangent bundle of a differentiable manifold consists, at every point of the manifold, of the dual of the tangent space, the cotangent space.

    Vector space

    Vector space

    Vector_space

  • Weierstrass functions
  • Mathematical functions related to Weierstrass's elliptic function

    to that between the sine, cotangent, and squared cosecant functions: the logarithmic derivative of the sine is the cotangent, whose derivative is negative

    Weierstrass functions

    Weierstrass_functions

  • Serre duality
  • Theorem in algebraic geometry

    K_{X}} to be the bundle of n-forms on X, the top exterior power of the cotangent bundle: K X = Ω X n = ⋀ n ( T ∗ X ) . {\displaystyle K_{X}=\Omega _{X}^{n}={\bigwedge

    Serre duality

    Serre_duality

  • Hyperkähler manifold
  • Type of Riemannian manifold

    showed the more general statement that cotangent bundle T ∗ C P n {\displaystyle T^{*}\mathbb {CP} ^{n}} of any complex projective space has a complete hyperkähler

    Hyperkähler manifold

    Hyperkähler_manifold

  • H-object
  • contravariant functor with values in Abelian groups. André–Quillen cohomology Cotangent complex H-space Quillen, Dan. "On the (co-) homology of commutative rings"

    H-object

    H-object

  • Atiyah–Singer index theorem
  • Mathematical result in differential geometry

    coordinate charts, and is a function on the cotangent bundle of X, homogeneous of degree n on each cotangent space. (In general, differential operators

    Atiyah–Singer index theorem

    Atiyah–Singer_index_theorem

  • Tangent space
  • Assignment of vector fields to manifolds

    I / I 2 {\displaystyle I/I^{2}} can be shown to be isomorphic to the cotangent space T x ∗ M {\displaystyle T_{x}^{*}M} through the use of Taylor's theorem

    Tangent space

    Tangent_space

  • Imaginary unit
  • Principal square root of minus 1

    Euler expressed the partial fraction decomposition of the trigonometric cotangent as π cot ⁡ π z = 1 z + 1 z − 1 + 1 z + 1 + 1 z − 2 + 1 z + 2 + ⋯ . {\textstyle

    Imaginary unit

    Imaginary unit

    Imaginary_unit

  • Laplace operators in differential geometry
  • Elliptic differential operators in geometry mathematics

    (Abstractly, it is a second order operator on each exterior power of the cotangent bundle.) This operator is defined on any manifold equipped with a Riemannian-

    Laplace operators in differential geometry

    Laplace_operators_in_differential_geometry

  • Hodge theory
  • Mathematical manifold theory

    extending (see Gramian matrix) the inner product induced by g from each cotangent fiber T p ∗ ( M ) {\displaystyle T_{p}^{*}(M)} to its k t h {\displaystyle

    Hodge theory

    Hodge_theory

  • Quadratic differential
  • the cotangent space to the Riemann moduli space, or Teichmüller space. Each quadratic differential on a domain U {\displaystyle U} in the complex plane

    Quadratic differential

    Quadratic_differential

  • Trigonometry
  • Area of geometry, about angles and lengths

    mathematician Habash al-Hasib al-Marwazi produced the first table of cotangents. By the 10th century AD, in the work of Persian mathematician Abū al-Wafā'

    Trigonometry

    Trigonometry

    Trigonometry

  • Calabi–Yau manifold
  • Riemannian manifold with SU(n) holonomy

    the fibers of the vector bundle. Using this, we can use the relative cotangent sequence 0 → p ∗ Ω C → Ω V → Ω V / C → 0 {\displaystyle 0\to p^{*}\Omega

    Calabi–Yau manifold

    Calabi–Yau manifold

    Calabi–Yau_manifold

  • Differential operator
  • Typically linear operator defined in terms of differentiation of functions

    principal symbol is intrinsically defined (i.e., it is a function on the cotangent bundle). More generally, let E and F be vector bundles over a manifold

    Differential operator

    Differential operator

    Differential_operator

  • Holomorphic vector bundle
  • Complex vector bundle on a complex manifold

    examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic cotangent bundle. A holomorphic line bundle is a rank one

    Holomorphic vector bundle

    Holomorphic_vector_bundle

  • Configuration space (physics)
  • Space of possible positions for all objects in a physical system

    the velocities of the points q ∈ Q {\displaystyle q\in Q} , while the cotangent space T ∗ Q {\displaystyle T^{*}Q} corresponds to momenta. (Velocities

    Configuration space (physics)

    Configuration_space_(physics)

  • List of mathematical abbreviations
  • inverse cosecant function. (Also written as arccsc.) arccot – inverse cotangent function. arccsc – inverse cosecant function. (Also written as arccosec

    List of mathematical abbreviations

    List_of_mathematical_abbreviations

  • Symplectic vector space
  • Mathematical concept

    an n-manifold, considered as a 2n-manifold, has an almost complex structure, and the cotangent bundle of an n-manifold, considered as a 2n-manifold, has

    Symplectic vector space

    Symplectic_vector_space

  • Tautological one-form
  • Canonical differential form

    mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle T ∗ Q {\displaystyle T^{*}Q} of a manifold Q . {\displaystyle Q

    Tautological one-form

    Tautological_one-form

  • Integration by substitution
  • Technique in integral evaluation

    \left|\cos x\right|+C\\&=\ln \left|\sec x\right|+C.\end{aligned}}} The cotangent function can be integrated similarly by expressing it as cot ⁡ x = cos

    Integration by substitution

    Integration_by_substitution

  • Teichmüller space
  • Parametrizes complex structures on a surface

    differentials on a Riemann surface X {\displaystyle X} are identified with the cotangent space at ( X , f ) {\displaystyle (X,f)} to Teichmüller space. The Weil–Petersson

    Teichmüller space

    Teichmüller_space

  • Canonical bundle
  • Concept in algebraic geometry

    {\displaystyle n} th exterior power of the cotangent bundle Ω {\displaystyle \Omega } on V {\displaystyle V} . Over the complex numbers, it is the determinant bundle

    Canonical bundle

    Canonical_bundle

  • CR manifold
  • Differentiable manifold

    characterized in terms of duality. Consider the line subbundle of the complex cotangent bundle annihilating V H 0 M = V ∗ = ( L ⊕ L ¯ ) ⊥ ⊂ T ∗ M ⊗ C . {\displaystyle

    CR manifold

    CR_manifold

  • Atiyah–Hirzebruch spectral sequence
  • for all (complex) even dimensional smooth complete intersections in C P n {\displaystyle \mathbb {CP} ^{n}} . For example, consider the cotangent bundle

    Atiyah–Hirzebruch spectral sequence

    Atiyah–Hirzebruch_spectral_sequence

  • List of differential geometry topics
  • manifold Tensor analysis Tangent vector Tangent space Tangent bundle Cotangent space Cotangent bundle Tensor Tensor bundle Vector field Tensor field Differential

    List of differential geometry topics

    List_of_differential_geometry_topics

  • Heron's formula
  • Triangle area in terms of side lengths

    }{2}}\cot {\tfrac {\beta }{2}}\cot {\tfrac {\gamma }{2}}} , the triple cotangent identity, which applies because the sum of half-angles is α 2 + β 2 +

    Heron's formula

    Heron's formula

    Heron's_formula

  • Chern class
  • Characteristic classes of vector bundles

    0}dz_{i}-z_{i}dz_{0} \over z_{0}^{2}},\,i\geq 1.} In other words, the cotangent sheaf Ω C P n | U {\displaystyle \Omega _{\mathbb {C} \mathbb {P} ^{n}}|_{U}}

    Chern class

    Chern_class

  • Descartes' theorem
  • Equation for radii of tangent circles

    geodesic curvature of the circle relative to the sphere, which equals the cotangent of the oriented intrinsic radius ρ j . {\displaystyle \rho _{j}.} Then:

    Descartes' theorem

    Descartes' theorem

    Descartes'_theorem

  • Glossary of differential geometry and topology
  • Connected sum Connection Cotangent bundle – the vector bundle of cotangent spaces on a manifold. Cotangent space Covering Cusp CW-complex Dehn twist Diffeomorphism

    Glossary of differential geometry and topology

    Glossary_of_differential_geometry_and_topology

  • Multiplicative inverse
  • Number which when multiplied by x equals 1

    The trigonometric functions are related by the reciprocal identity: the cotangent is the reciprocal of the tangent; the secant is the reciprocal of the

    Multiplicative inverse

    Multiplicative inverse

    Multiplicative_inverse

  • Courant bracket
  • It is a generalization of the Lie bracket from an operation on the tangent bundle

    transformation is known in the physics literature as a shift in the B field. The cotangent bundle, T ∗ {\displaystyle {\mathbf {T} }^{*}} of M {\displaystyle M}

    Courant bracket

    Courant_bracket

  • Kähler identities
  • \beta \rangle } is the inner product on the exterior products of the cotangent space of X {\displaystyle X} induced by the Riemannian metric. Using this

    Kähler identities

    Kähler_identities

  • D-module
  • Module over a sheaf of differential operators

    the symbols, which in the good case is a Lagrangian submanifold of the cotangent bundle of maximal dimension (involutive systems). The techniques were

    D-module

    D-module

  • Symplectic resolution
  • Mathematical concept

    varieties and their cotangent bundles. In the 21st century, this approach evolved into a more general framework where the traditional cotangent bundle of the

    Symplectic resolution

    Symplectic_resolution

  • Metric tensor
  • Structure defining distance on a manifold

    that g⊗ is regarded also as a section of the bundle T*M ⊗ T*M of the cotangent bundle T*M with itself. Since g is symmetric as a bilinear mapping, it

    Metric tensor

    Metric_tensor

  • Modern Arabic mathematical notation
  • Mathematical notation based on the Arabic script

    is used in some regions (e.g. Syria); Arabic for "tangent" is ظل ẓill Cotangent cot {\displaystyle \cot } طتا from طتا ṭāʾ (i.e. dotless ظ ẓāʾ)-tāʾ-ʾalif;

    Modern Arabic mathematical notation

    Modern_Arabic_mathematical_notation

  • Eguchi–Hanson space
  • Concept in mathematics and theoretical physics

    non-compact, self-dual, asymptotically locally Euclidean (ALE) metric on the cotangent bundle of the 2-sphere T*S2. The holonomy group of this 4-real-dimensional

    Eguchi–Hanson space

    Eguchi–Hanson_space

  • Phase space
  • Space of all possible states that a system can take

    phase space. More abstractly, in classical mechanics phase space is the cotangent bundle of configuration space, and in this interpretation the procedure

    Phase space

    Phase space

    Phase_space

  • Contact geometry
  • Branch of geometry

    elements of M {\displaystyle M} can be identified with a quotient of the cotangent bundle T ∗ M {\displaystyle T^{*}M} (with the zero section 0 M {\displaystyle

    Contact geometry

    Contact_geometry

  • Analytic space
  • vanishing at x, then the cotangent space at x is mx / mx2. The tangent space is (mx / mx2)*, the dual vector space to the cotangent space. Analytic mappings

    Analytic space

    Analytic_space

  • Functor
  • Mapping between categories

    T ∗ M ) {\displaystyle \Gamma {\mathord {\left(T^{*}M\right)}}} of a cotangent bundle T ∗ M {\displaystyle T^{*}M} —as "covariant". This terminology

    Functor

    Functor

  • Nonabelian Hodge correspondence
  • Correspondsnce between Higgs bundles and fundamental group representations

    structure on the cotangent bundle to the Jacobian. It is possible to define the notion of a principal G {\displaystyle G} -Higgs bundle for a complex reductive

    Nonabelian Hodge correspondence

    Nonabelian_Hodge_correspondence

  • Kentaro Yano (mathematician)
  • Japanese mathematician

    Geometry, Marcel Dekker, New York 1970 with Shigeru Ishihara: Tangent and cotangent bundles: differential geometry, New York, M. Dekker 1973 with Masahiro

    Kentaro Yano (mathematician)

    Kentaro_Yano_(mathematician)

  • Poisson manifold
  • Mathematical structure in differential geometry

    -dimensional smooth manifold Q {\displaystyle Q} , and the phase space is its cotangent bundle T ∗ Q {\displaystyle T^{*}Q} (a manifold of dimension 2 n {\displaystyle

    Poisson manifold

    Poisson_manifold

  • Differential form
  • Expression that may be integrated over a region

    a smooth section of the k {\displaystyle k} th exterior power of the cotangent bundle of M {\displaystyle M} . The set of all differential k {\displaystyle

    Differential form

    Differential_form

  • Hermite's cotangent identity
  • Mathematical formula

    mathematics, Hermite's cotangent identity is a trigonometric identity discovered by Charles Hermite. Suppose a1, ..., an are complex numbers, no two of which

    Hermite's cotangent identity

    Hermite's_cotangent_identity

  • Line bundle
  • Vector bundle of rank 1

    {\displaystyle V} . This construction is in particular applied to the cotangent bundle of a smooth manifold. The resulting determinant bundle (more precisely

    Line bundle

    Line_bundle

  • List of things named after Charles Hermite
  • stably free module is free of unique rank Hermite-Sobolev spaces Hermite's cotangent identity, a trigonometric identity Hermite's criterion Hermite's identity

    List of things named after Charles Hermite

    List_of_things_named_after_Charles_Hermite

  • Lemniscate elliptic functions
  • Mathematical functions

    hyperbolic lemniscate sine and cosine are analogous to the tangent and cotangent functions in a unit circle x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1}

    Lemniscate elliptic functions

    Lemniscate elliptic functions

    Lemniscate_elliptic_functions

  • Adjunction formula
  • Concept in algebraic geometry

    {I}}^{2}\to i^{*}\Omega _{X}\to \Omega _{Y}\to 0,} where Ω denotes a cotangent bundle. The determinant of this exact sequence is a natural isomorphism

    Adjunction formula

    Adjunction_formula

  • Yang–Mills equations
  • Partial differential equations whose solutions are instantons

    Since X {\displaystyle X} is Riemannian, there is an inner product on the cotangent bundle, and combined with the invariant inner product on ad ⁡ ( P ) {\displaystyle

    Yang–Mills equations

    Yang–Mills equations

    Yang–Mills_equations

  • Hopf bifurcation
  • Critical point where a periodic solution arises

    given by a Lie derivative defined on the tangent bundle. Because all cotangent bundles are always symplectic manifolds, it is common to formulate bifurcation

    Hopf bifurcation

    Hopf bifurcation

    Hopf_bifurcation

  • Microdifferential operator
  • In mathematics, a microdifferential operator is a linear operator on a cotangent bundle (phase space) that generalizes a differential operator and appears

    Microdifferential operator

    Microdifferential_operator

  • Jean-Claude Sikorav
  • French mathematician

    Laudenbach, of the Arnold conjecture for Lagrangian intersections in cotangent bundles, as well as for introducing generating families in symplectic

    Jean-Claude Sikorav

    Jean-Claude Sikorav

    Jean-Claude_Sikorav

  • History of trigonometry
  • fully established all six trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant) with complete proofs, and formulated the plane and

    History of trigonometry

    History of trigonometry

    History_of_trigonometry

  • Hitchin system
  • Type of integrable system

    geometry, the phase space of the system is a partial compactification of the cotangent bundle to the moduli space of stable G-bundles for some reductive group

    Hitchin system

    Hitchin_system

  • Rhind Mathematical Papyrus
  • Ancient Egyptian mathematical document

    of its face. In other words, the quantity found for the seked is the cotangent of the angle to the base of the pyramid and its face. The third part of

    Rhind Mathematical Papyrus

    Rhind Mathematical Papyrus

    Rhind_Mathematical_Papyrus

  • Coherent sheaf
  • Generalization of vector bundles

    _{X/k}^{1}} ) is a vector bundle over X {\displaystyle X} , called the cotangent bundle of X {\displaystyle X} . Then the tangent bundle T X {\displaystyle

    Coherent sheaf

    Coherent_sheaf

  • Polygamma function
  • Meromorphic function

    ⁠1/2⁠, i.e. the Bernoulli numbers of the second kind. The hyperbolic cotangent satisfies the inequality t 2 coth ⁡ t 2 ≥ 1 , {\displaystyle {\frac {t}{2}}\operatorname

    Polygamma function

    Polygamma function

    Polygamma_function

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Online names & meanings

  • Zebudah
  • Girl/Female

    Biblical

    Zebudah

    Endowed, endowing.

  • USUR-T-KAU
  • Female

    Egyptian

    USUR-T-KAU

    , The Most Powerful of Beings.

  • Dahi
  • Boy/Male

    Indian

    Dahi

    Lion, Rapid

  • Madhumitha
  • Girl/Female

    Hindu

    Madhumitha

    Full of Honey, Sweet person

  • Talford
  • Surname or Lastname

    English (South Yorkshire)

    Talford

    English (South Yorkshire) : variant of Telford.

  • Frazier
  • Boy/Male

    Australian, British, Christian, English, French, Scottish

    Frazier

    French Town; Curly Hair; Strawberry; Of the Forest Men; Variant of Fraser

  • Rachyaita
  • Girl/Female

    Indian

    Rachyaita

    Creator; Artist

  • Mussey
  • Surname or Lastname

    English

    Mussey

    English : nickname from Middle English mūs ‘mouse’ + ēage ‘eye’.Possibly an altered spelling of French Musset (see Mussett 1).

  • Sidhu
  • Boy/Male

    Hindu

    Sidhu

  • Zaanannim
  • Biblical

    Zaanannim

    movings; a person asleep

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  • Eventtual
  • a.

    Dependent on events; contingent.

  • Contingent
  • n.

    That which falls to one in a division or apportionment among a number; a suitable share; proportion; esp., a quota of troops.

  • Contingent
  • a.

    Possible, or liable, but not certain, to occur; incidental; casual.

  • Tangentially
  • adv.

    In the direction of a tangent.

  • Tangent
  • a.

    Touching; touching at a single point

  • Tangent
  • a.

    meeting a curve or surface at a point and having at that point the same direction as the curve or surface; -- said of a straight line, curve, or surface; as, a line tangent to a curve; a curve tangent to a surface; tangent surfaces.

  • Contingentness
  • n.

    The state of being contingent; fortuitousness.

  • Tangent
  • v. t.

    A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced. See Trigonometrical function, under Function.

  • Semitangent
  • n.

    The tangent of half an arc.

  • Contingent
  • a.

    Dependent for effect on something that may or may not occur; as, a contingent estate.

  • Cotangent
  • n.

    The tangent of the complement of an arc or angle. See Illust. of Functions.

  • Contingent
  • n.

    An event which may or may not happen; that which is unforeseen, undetermined, or dependent on something future; a contingency.

  • Bitangent
  • a.

    Possessing the property of touching at two points.

  • Mesologarithm
  • n.

    A logarithm of the cosine or cotangent.

  • Contingently
  • adv.

    In a contingent manner; without design or foresight; accidentally.

  • Expectative
  • a.

    Constituting an object of expectation; contingent.

  • Contingent
  • a.

    Dependent on that which is undetermined or unknown; as, the success of his undertaking is contingent upon events which he can not control.

  • Tangential
  • a.

    Of or pertaining to a tangent; in the direction of a tangent.

  • Bitangent
  • n.

    A line that touches a curve in two points.

  • Touch
  • v. t.

    To be tangent to. See Tangent, a.