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Describes the transverse intersection properties of a smooth family of smooth maps
In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result
Transversality_theorem
Description of how spaces intersect in mathematics
In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays
Transversality
French mathematician (1923–2002)
spaces, characteristic classes, cobordism theory, and the Thom transversality theorem. Another example of this line of work is the Thom conjecture, versions
René_Thom
Stratifiability condition in mathematical topology
dense by Thom's transversality theorem. The density of the set of transverse mappings is often interpreted by saying that transversality is a 'generic'
Whitney_conditions
Topological space associated to a vector bundle
on and is intimately related to the transversality properties of smooth manifolds—see Thom transversality theorem. By reversing this construction, John
Thom_space
Swan's theorem (module theory) Tameness theorem (3-manifolds) Thom transversality theorem (differential topology) Thurston's geometrization theorem (3-manifolds)
List_of_theorems
Unsolved problem in geometry
which were introduced by Henri Poincaré. However, the Griffiths transversality theorem shows that this approach cannot prove the Hodge conjecture for higher
Hodge_conjecture
Result in combinatorics and graph theory
mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and
Hall's_marriage_theorem
Certain vector fields are the sum of an irrotational and a solenoidal vector field
In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector
Helmholtz_decomposition
Line intersecting 2 coplanar lines at 2 points
corresponding angles of any transversal are congruent (equal in measure). Proposition 1.28 of Euclid's Elements, a theorem of absolute geometry (hence
Transversal_(geometry)
Moduli space of the Seiberg–Witten equations
99, Theorem 2.4.24 Nicoleascu 2000, Lemma 2.2.10. Perutz 2002, p. 10 Kronheimer & Mrowka 2007, Theorem 1.4.4. Moore 2010, Transversality Theorem 2 on
Seiberg–Witten_moduli_space
Theorem in quantum computing
Eastin–Knill theorem is a no-go theorem that states: "No quantum error correcting code can have a continuous symmetry which acts transversely on physical
Eastin–Knill_theorem
Operation in differential geometry
of jets over different base-points. Mather proved the multijet transversality theorem, which he used in his study of stable mappings. Suppose that E is
Jet_(mathematics)
Theorem in differential topology
^{2m}} with transverse self-intersections. These are known to exist from Whitney's earlier work on the weak immersion theorem. Transversality of the double
Whitney_embedding_theorem
Theorem in mathematics
MR 3310023. Zbl 1300.26003. Spivak 1965, Theorem 2-12. Spivak 1965, Theorem 5-1. and Theorem 2-13. "Transversality" (PDF). northwestern.edu. One of Spivak's
Inverse_function_theorem
on Xb. Griffiths proved that the period map is holomorphic. His transversality theorem limits the range of the period map. The Hodge filtration can be
Period_mapping
Fixed-point theorem for smooth manifolds
of f. Counting codimensions in M × M {\displaystyle M\times M} , a transversality assumption for the graph of f and the diagonal should ensure that the
Atiyah–Bott fixed-point theorem
Atiyah–Bott_fixed-point_theorem
Algebraic geometry theorem
Théorèmes de Bertini et applications. Boston, MA: Birkhäuser Boston, Inc. p. 89. ISBN 0-8176-3164-X. Kleiman, Steven L. (1974), "The transversality of
Theorem_of_Bertini
Brouwer". René Thom (1954) In this paper, Thom proved the Thom transversality theorem, introduced the notions of oriented and unoriented cobordism, and
List of publications in mathematics
List_of_publications_in_mathematics
Mathematical result in differential geometry
index theorem on topological manifolds", Acta Mathematica, 153: 117–152, doi:10.1007/BF02392376, Zbl 0547.58036 Teleman, N. (1985), "Transversality and
Atiyah–Singer_index_theorem
Theorem about triangles
In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle △ABC, let the lines AO, BO, CO be drawn from the vertices to a common
Ceva's_theorem
Theorem about the intersections of d-dimensional convex sets
Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published
Helly's_theorem
Theorem in geometry about convex sets
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that: Any set of d + 2 points in Rd can be partitioned into two
Radon's_theorem
Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P
Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle
Carathéodory's theorem (convex hull)
Carathéodory's_theorem_(convex_hull)
Theorem in differential topology
constraint). The weak version, for 2 m + 1 {\displaystyle 2m+1} , is due to transversality (general position, dimension counting): two m-dimensional manifolds
Whitney_immersion_theorem
Theorem in symplectic topology
bubble is a holomorphic sphere which has a transverse intersection with the rest of the curve. This theorem, and its generalizations to punctured pseudoholomorphic
Gromov's compactness theorem (topology)
Gromov's_compactness_theorem_(topology)
Littlewood–Richardson rule. For algebro-geometric reasons (Kleiman's transversality theorem of 1974), these coefficients are non-negative integers and it is
Schubert_polynomial
Book on old philosophy by Avicenna
benefit of logic Types of particles Intrinsic and transversal Theorem and its types Material of theorems Directions, inversion, analogy and its types Trilogy
Al-Nijat
On when elements of the 2nd homotopy group of a 3-manifold can be embedded spheres
theorem can be based on transversality methods, see Jean-Loïc Batude (1971). Another more general version (also called the projective plane theorem,
Sphere_theorem_(3-manifolds)
Geometric relation on line segments formed by a line cutting through a triangle
Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle △ABC, and a transversal line
Menelaus's_theorem
measurement. Transversals have been replaced in modern times by vernier scales. This method is based on the Intercept theorem (also known as Thales's theorem). Transversals
Transversal (instrument making)
Transversal_(instrument_making)
American mathematician
order types and polytopes, and a generalization of the Hadwiger transversal theorem to higher dimensions. He and Goodman were the founding editors of
Richard_M._Pollack
On partitions into intersecting convex hulls
In discrete geometry, Tverberg's theorem, first stated by Helge Tverberg in 1966, is the result that sufficiently many points in Euclidean space can be
Tverberg's_theorem
In algebraic geometry, Kleiman's theorem, introduced by Kleiman (1974), concerns dimension and smoothness of scheme-theoretic intersection after some
Kleiman's_theorem
Branch of mathematics
immersions and submersions, and the intersections of submanifolds via transversality. More generally one is interested in properties and invariants of smooth
Differential_topology
Generalizations in graph theory
theory, Hall-type theorems for hypergraphs are several generalizations of Hall's marriage theorem from graphs to hypergraphs. Such theorems were proved by
Hall-type theorems for hypergraphs
Hall-type_theorems_for_hypergraphs
Extends the Jordan curve theorem to characterize the inner and outer regions
the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan curves
Schoenflies_problem
Geometric theorem involving midpoints on a triangle
The midpoint theorem, midsegment theorem, or midline theorem states that if the midpoints of two sides of a triangle are connected, then the resulting
Midpoint_theorem_(triangle)
Set that intersects every one of a family of sets
every partition has a transversal. A fundamental question in the study of SDR is whether or not an SDR exists. Hall's marriage theorem gives necessary and
Transversal_(combinatorics)
Graph divided into two independent sets
size of the maximum matching; this is Kőnig's theorem. An alternative and equivalent form of this theorem is that the size of the maximum independent set
Bipartite_graph
transversal plane may also form dihedral angles. Transversal plane theorem for lines: Lines that intersect a transversal plane are parallel if and only if their
Transversal_plane
Type of massless subatomic particle
pseudo-Goldstone bosons or pseudo–Nambu–Goldstone bosons. Goldstone's theorem examines a generic continuous symmetry which is spontaneously broken; i
Goldstone_boson
Doignon's theorem in geometry is an analogue of Helly's theorem for the integer lattice. It states that, if a family of convex sets in d {\displaystyle
Doignon's_theorem
American geometer (1933–2021)
of order types of polytopes, and a generalization of the Hadwiger transversal theorem to higher dimensions. He and Pollack were the founding editors of
Jacob_E._Goodman
Foundational law of classical magnetism
also referred to as the "transversality requirement" because for plane waves it requires that the polarization be transverse to the direction of propagation
Gauss's_law_for_magnetism
Theorem that every subgroup of a free group is itself free
In group theory, a branch of mathematics, the Nielsen–Schreier theorem states that every subgroup of a free group is itself free. It is named after Jakob
Nielsen–Schreier_theorem
Relationship between two lines that meet at a right angle
the SSS congruence theorem for QPA' and QPB' to conclude that angles OPA' and OPB' are equal. Then use the SAS congruence theorem for triangles OPA' and
Perpendicular
equilibrium points and hyperbolic periodic orbits and satisfying a transversality condition on the stable and unstable manifolds. Morse–Smale systems
Morse–Smale_system
Russian-Swedish mathematician
maint: archived copy as title (link) Purbhoo, Kevin (2009). "Reality and transversality for Schubert calculus in OG(n,2n+1)". arXiv:0911.2039 [math.AG]. Boris
Boris_Shapiro
Sums of sets of vectors are nearly convex
about how close the approximation is. For example, the Shapley–Folkman theorem provides an upper bound on the distance between any point in the Minkowski
Shapley–Folkman_lemma
Property of differential equations describing physical phenomena
differential equation are all made up of analytic functions and a certain transversality condition is satisfied (the hyperplane or more generally hypersurface
Well-posed_problem
Concept in mathematics
fundamental group. By a theorem of Hansklaus Rummler and Dennis Sullivan, the following conditions are equivalent for transversely orientable codimension
Taut_foliation
theorem is a theorem in general topology due to American mathematician James Dugundji. It is directly related to the Tietze–Urysohn extension theorem
Dugundji_extension_theorem
Map projection system
maps could be performed more easily in the field (using the Pythagorean theorem) than was possible using the trigonometric formulas required under the
Universal Transverse Mercator coordinate system
Universal_Transverse_Mercator_coordinate_system
Mathematical theory
In mathematics, Reeb stability theorem, named after Georges Reeb, asserts that if one leaf of a codimension-one foliation is closed and has finite fundamental
Reeb_stability_theorem
German mathematician
Cieliebak and A. Floer) Math. Zeit. 218, 103–122, 1995. Hofer, Helmut. Transversality results in the elliptic Morse theory of the action functional (jointly
Andreas_Floer
Special symmetric bilinear form on the 2nd (co)homology group of a 4-manifold
)\times H_{2}(M;\mathbb {Z} )\to \mathbb {Z} .} Using the notion of transversality, one can state the following results (which constitute an equivalent
Intersection form of a 4-manifold
Intersection_form_of_a_4-manifold
Concept in algebraic geometry
geometric topology, the analogous notion of transversality is used: subvarieties in general intersect transversally, meaning with multiplicity 1, rather than
General_position
English mathematician
characterization of transversal independence structures’. Bull. London Math. Soc. 3 (1971) 47–51. ‘Conditions for representability and transversality of matroids’
Aubrey_William_Ingleton
American mathematician
Grothendieck duality theory, Springer-Verlag. Kleiman, Steven L. (1974), "The transversality of a general translate", Compositio Mathematica, 28 (3): 287–297. Altman
Steven_Kleiman
Term in mathematics
addressed more closely. The hypersurfaces may be required to satisfy a transversality condition (like their tangent spaces being in general position at intersection
Complete_intersection
Neoclassical economic model
does arise because of Malinvaud's explicit inclusion of a so-called "transversality condition" (which Malinvaud calls Condition I) in his paper. At the
Ramsey–Cass–Koopmans_model
Mathematical space
density theorem for Kleinian groups and the ending lamination theorem. It also implies the Ahlfors measure conjecture. The ending lamination theorem, originally
3-manifold
Abstraction of disjoint paths in directed graphs
Ingleton–Piff Theorem, every gammoid is a contraction of a transversal matroid. The gammoids are the smallest class of matroids that includes the transversal matroids
Gammoid
Israeli physicist
analysis of "free ends" physical problems, enabling application of the "transversality conditions". In 1987 Dr. Bormashenko studied the mechanisms of destruction
Edward_Bormashenko
90° angle (π/2 radians)
four right angles, in addition to equal-length sides. The Pythagorean theorem states how to determine when a triangle is a right triangle. In Unicode
Right_angle
On when a manifold that admits a singular foliation is homeomorphic to the sphere
In mathematics, Reeb sphere theorem, named after Georges Reeb, states that A closed oriented connected manifold M n that admits a singular foliation having
Reeb_sphere_theorem
Axiom of set theory
by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. In many cases, a set created by choosing elements can be made without
Axiom_of_choice
Singularities of algebraic varieties
smooth, and any two of them intersect transversely, but the three together are not transverse. Transversality would imply that the intersection of more
Normal_crossing_singularity
Number used in algebraic geometry
intersections with multiplicity, as in Bézout's theorem). If two varieties Y and Z intersect transversally, then the degree of their intersection is the
Degree of an algebraic variety
Degree_of_an_algebraic_variety
Form of interpolation
{\sim }{\longrightarrow }}\,P(n).} This is a type of unisolvence theorem. The theorem is also valid over any infinite field in place of the real numbers
Polynomial_interpolation
Theorem of 2D geometry
In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes
Poncelet's_closure_theorem
British mathematician (1906–1989)
theory, the Erdős–Rado theorem extends Ramsey's theorem to infinite sets. It was published by Erdős and Rado in 1956. Rado's theorem is another Ramsey-theoretic
Richard_Rado
Connects homology and cohomology groups for oriented closed manifolds
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of
Poincaré_duality
German polymath and scholar (1777–1855)
Gauss produced the second and third complete proofs of the fundamental theorem of algebra. He also introduced the triple bar symbol (≡) for congruence
Carl_Friedrich_Gauss
Ancient Greek mathematician (fl. 300 BC)
the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections
Euclid
Vector field with zero divergence
property is to say that the field has no sources or sinks. The divergence theorem gives an equivalent integral definition of a solenoidal field; namely that
Solenoidal_vector_field
space Thom space Torus Transversality – Two submanifolds M {\displaystyle M} and N {\displaystyle N} intersect transversally if at each point of intersection
Glossary of differential geometry and topology
Glossary_of_differential_geometry_and_topology
Natural number
2020-08-07. Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory Volume I: Tools and Diophantine Equations. Graduate Texts
7
Calculus of functions generalization
concepts from differential geometry such as differential forms and Stokes' theorem. This extensive use of linear algebra also allows a natural generalization
Calculus_on_Euclidean_space
also be deflected by magnetic fields (see Panofsky-Wenzel theorem). Because the transverse deflection can be described with polar coordinates, one may
Shunt_impedance
In mathematics, a partition of a manifold into submanifolds
{F}}} is transverse to N, and every flow line meets N. Because the dimensions of N and of the leaves are complementary, the transversality condition
Foliation
Complexity class of problems
NP-intermediate, and the class of such problems is called NPI. Ladner's theorem, shown in 1975 by Richard E. Ladner, is a result asserting that, if P ≠
NP-intermediate
refinement theorem Subgroup Transversal (combinatorics) Torsion subgroup Zassenhaus lemma Automorphism Automorphism group Factor group Fundamental theorem on
List_of_group_theory_topics
In mathematics, Harish-Chandra's regularity theorem, introduced by Harish-Chandra (1963), states that every invariant eigendistribution on a semisimple
Harish-Chandra's regularity theorem
Harish-Chandra's_regularity_theorem
Geometry without the parallel postulate
interior angle theorem, l is parallel to n. (The alternate interior angle theorem states that if lines a and b are cut by a transversal t such that there
Absolute_geometry
Statistical model in quantum mechanics of magnetic materials
}-{\frac {1}{2}}\cos 2\eta 1^{\otimes N}.} The Lieb-Schultz-Mattis (LSM) theorem demonstrates that in a one-dimensional antiferromagnetic Heisenberg model
Quantum_Heisenberg_model
Concept in mathematics
Theorem 6.4. Farb & Margalit 2012, Theorem 6.15 and Theorem 6.12. Farb & Margalit 2012, Theorem 6.11. Ivanov 1992, Theorem 4. Ivanov 1992, Theorem 1
Mapping class group of a surface
Mapping_class_group_of_a_surface
Graph with tight clique-coloring relation
important minimax theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem on partially ordered sets, Kőnig's theorem on matchings, and
Perfect_graph
Function used in optimal control theory
and Transversality Conditions". Optimal Control Theory and Static Optimization in Economics. New York: Cambridge University Press. p. 222 [Theorem 7.1
Hamiltonian_(control_theory)
Problem-solving technique in geometry
{3}{13}}={\tfrac {7}{26}}.} Cevian Ceva's theorem Menelaus's theorem Stewart's theorem Angle bisector theorem Routh's theorem Barycentric coordinates Lever Rhoad
Mass_point_geometry
Mathematical problem
MacNeish's theorem does not give a very good lower bound, for instance if n ≡ 2 (mod 4), that is, there is a single 2 in the prime factorization, the theorem gives
Mutually orthogonal Latin squares
Mutually_orthogonal_Latin_squares
Mod 2 invariant of (4k+1)-dimensional manifold
semicharacteristic. Morgan, John W; Sullivan, Dennis P. (1974), "The transversality characteristic class and linking cycles in surgery theory", Annals of
De_Rham_invariant
Statistical mechanics model for phase transitions
{\displaystyle z\equiv \exp(-2\beta h)} . This statement is known as the Lee–Yang theorem, and has later been generalized to other models, such as the Heisenberg
Lee–Yang_theory
Concept in mathematics
by the work of Andronov and Pontryagin, developed and proved Peixoto's theorem, the first global characterization of structural stability. Let G be an
Structural_stability
Concept in algebraic geometry
used a more roundabout method: he first proved a local uniformization theorem showing that every valuation of a surface could be resolved, then used
Resolution_of_singularities
2021) Duffin–Schaeffer theorem (Dimitris Koukoulopoulos, James Maynard, 2019) Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Convex, 4-sided shape with an incircle and a circumcircle
a, b, c, d is bicentric if and only if opposite sides satisfy Pitot's theorem for tangential quadrilaterals and the cyclic quadrilateral property that
Bicentric_quadrilateral
Set of hypergraph nodes to which every hyperedge is connected
of a hypergraph is, in general, smaller than its vertex-cover-number. A theorem of László Lovász provides an upper bound on the ratio between them: If
Vertex_cover_in_hypergraphs
Theorem in group theory
In group theory, Schreier's lemma is a theorem used in the Schreier–Sims algorithm and also for finding a presentation of a subgroup. Suppose H {\displaystyle
Schreier's_lemma
TRANSVERSALITY THEOREM
TRANSVERSALITY THEOREM
TRANSVERSALITY THEOREM
TRANSVERSALITY THEOREM
Boy/Male
Hindu, Indian
Part of Lady and Man; Slove
Female
Scottish
Feminine form of Scottish Gaelic Domhnall, DOILEAG means "world ruler."
Boy/Male
Tamil
Hridyansh | ரீதà¯à®¯à®¾à®‚à®·
Piece of heart
Boy/Male
Arabic, Muslim, Sindhi
Companion; Narrator of Hadith; Ibn Sad Al-taiy had this Name; Al-tamimi RA also had this Name
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Great Intelligence
Girl/Female
Hindu, Indian, Kannada, Marathi, Sindhi, Tamil, Telugu
A Bird
Girl/Female
Spanish
Grace. favor.
Male
English
Anglicized form of Hebrew unisex Eyphah, EPHAH means "darkness" or "gloomy." In the bible, this is the name of several characters, including a son of Midian and one of Caleb's concubines.
Boy/Male
Tamil
Red lotus, Bright, Goddess Parvati
Male
English
Bard or Minstrel
TRANSVERSALITY THEOREM
TRANSVERSALITY THEOREM
TRANSVERSALITY THEOREM
TRANSVERSALITY THEOREM
TRANSVERSALITY THEOREM
n.
That which is considered and established as a principle; hence, sometimes, a rule.
v. t.
To formulate into a theorem.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
n.
A statement of a principle to be demonstrated.
a.
Alt. of Theorematical
a.
Theorematic.
n.
A numerical coefficient in any particular case of the binomial theorem.
n.
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.
n.
A theorem or proposition so easy of demonstration as to be almost self-evident.
n.
One who constructs theorems.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.