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Theorem in differential geometry
various splitting theorems on when a pseudo-Riemannian manifold can be given as a metric product. The best-known is the Cheeger–Gromoll splitting theorem for
Splitting_theorem
Theory of hyperbolic spacetimes
theory of causal structure on Lorentzian manifolds, Geroch's theorem or Geroch's splitting theorem (first proved by Robert Geroch) gives a topological characterization
Geroch's_splitting_theorem
Topics referred to by the same term
Tongue splitting Heegaard splitting Splitting field Splitting principle Splitting theorem Splitting lemma Matrix splitting for the numerical method to
Splitting
Spacetime manifold
"leakage" of information or energy described above. The fundamental splitting theorem by Geroch (1970) establishes the equivalence between global hyperbolicity
Globally_hyperbolic_spacetime
Describes statistically the splitting of primes in a given Galois extension of Q
number theory, the Chebotarev density theorem, named after Nikolai Chebotarev, statistically describes the splitting of primes in a given Galois extension
Chebotarev_density_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Mathematical structure in differential geometry
also in the non-regular case, one can use Weinstein splitting theorem (or Darboux-Weinstein theorem). It states that any Poisson manifold ( M n , π ) {\displaystyle
Poisson_manifold
American mathematical physicist (b. 1942)
Biography portal Physics portal Geroch energy Geroch group Geroch's splitting theorem GHP formalism American Men and Women of Science, Thomson Gale, 2004
Robert_Geroch
Branch of differential geometry
equality if and only if the Riemannian manifold is a flat torus. Splitting theorem. If a complete n-dimensional Riemannian manifold has nonnegative Ricci
Riemannian_geometry
Theorem about Turing reductions
In mathematical logic, the Friedberg–Muchnik theorem is a theorem about Turing reductions that was proven independently by Albert Muchnik and Richard Friedberg
Friedberg–Muchnik_theorem
Every Riemannian manifold can be isometrically embedded into some Euclidean space
The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded
Nash_embedding_theorems
American mathematician
(graph theory) Cheeger–Müller theorem Collapsing manifold L² cohomology Riemannian geometry Soul theorem Splitting theorem Faculty Profile 1984 U.S. and
Jeff_Cheeger
German mathematician (1938–2008)
Abresch–Gromoll inequality Gromoll–Meyer sphere Rational homotopy theory Splitting theorem Soul theorem Gromoll, Detlef; Klingenberg, Wilhelm; Meyer, Wolfgang (1968)
Detlef_Gromoll
Equations of degree 5 or higher cannot be solved by radicals
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial
Abel–Ruffini_theorem
Mathematical problem
Hobby–Rice theorem, and it is used to get an exact division of a cake. Each problem can be solved by the next problem: Discrete splitting can be solved
Necklace_splitting_problem
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Mathematical technique for vector bundles
Then the splitting principle can be quite useful. One version of the splitting principle is captured in the following theorem. This theorem holds for
Splitting_principle
Decomposition of a compact oriented 3-manifold by dividing it into two handlebodies
follows from Waldhausen's Theorem that every reducible splitting of an irreducible manifold is stabilized. A Heegaard splitting is weakly reducible if there
Heegaard_splitting
Group of mathematical theorems
specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients
Isomorphism_theorems
In linear algebra, relation between 3 dimensions
T)+\dim(\operatorname {Ker} T)=\dim(\operatorname {Domain} (T)).} This theorem can be refined via the splitting lemma to be a statement about an isomorphism of spaces
Rank–nullity_theorem
Tensor in differential geometry
the key point in the proof of Gromov's compactness theorem. The Cheeger–Gromoll splitting theorem states that if a complete Riemannian manifold ( M ,
Ricci_curvature
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no group decision-making
Arrow's_impossibility_theorem
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Classifies holomorphic vector bundles over the complex projective line
In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic
Birkhoff–Grothendieck_theorem
Field theory theorem
primitive element theorem states that every finite separable field extension is simple, i.e. generated by a single element. This theorem implies in particular
Primitive_element_theorem
Tool for analyzing divide-and-conquer algorithms
In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for many recurrence relations that
Master theorem (analysis of algorithms)
Master_theorem_(analysis_of_algorithms)
Russian mathematician
transformation are named after him. He also proved the first version of the splitting theorem. Stefan Cohn-Vossen was born 28 May, 1902 to Emanuel Cohn, a lawyer
Stefan_Cohn-Vossen
About direct sums and exact sequences
In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements are equivalent
Splitting_lemma
Vampire is an automatic theorem prover for first-order classical logic developed in the Department of Computer Science at the University of Manchester
Vampire_(theorem_prover)
Chinese-American mathematician (born 1949)
splitting theorem says that the splitting of the fundamental group as a maximally noncommutative direct product implies the isometric splitting of the manifold
Shing-Tung_Yau
Theorem in group theory
{\displaystyle G} ) for obtaining an actual splitting from a semi-splitting. It is also possible to prove Stallings' theorem for finitely presented groups using
Stallings theorem about ends of groups
Stallings_theorem_about_ends_of_groups
Type of geometry in mathematics
this class is flat, which is a corollary of Cheeger and Gromoll's splitting theorem. On a simply-connected Kähler manifold, a Kähler metric is Ricci-flat
Ricci-flat_manifold
Submanifold of Lorentzian manifold
N.; Sánchez, Miguel. On smooth Cauchy hypersurfaces and Geroch's splitting theorem. Comm. Math. Phys. 243 (2003), no. 3, 461–470. Bernal, Antonio N.;
Cauchy_surface
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
Bound on eigenvalues
In mathematics, the Gershgorin circle theorem (also called Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix. It was first
Gershgorin_circle_theorem
Theorem in graph theory
Euler tour by repeatedly splitting the tour into smaller cycles whenever there is a repeated vertex. However, Veblen's theorem applies also to disconnected
Veblen's_theorem
Theorem in quantum physics
In quantum electrodynamics, Furry's theorem states that if a Feynman diagram consists of a closed loop of fermion lines with an odd number of vertices
Furry's_theorem
Necklace splitting problem
In mathematics, and in particular the necklace splitting problem, the Hobby–Rice theorem is a result that is useful in establishing the existence of certain
Hobby–Rice_theorem
Operation in calculus
this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides
Integral
equation Frobenius splitting Frobenius theorem (differential topology) Frobenius theorem (real division algebras) Frobenius's theorem (group theory) Frobenius
List of things named after Ferdinand Georg Frobenius
List_of_things_named_after_Ferdinand_Georg_Frobenius
Root-finding algorithm for polynomials
The fundamental idea of the splitting circle method is to use methods of complex analysis, more precisely the residue theorem, to construct factors of polynomials
Splitting_circle_method
On representability of a contravariant functor on the category of connected CW complexes
In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy
Brown's representability theorem
Brown's_representability_theorem
Finite dimensional algebra over a field whose central elements are that field
then a maximal subfield of A is a splitting field. In general by theorems of Wedderburn and Koethe there is a splitting field which is a separable extension
Central_simple_algebra
Theorem that any three objects in space can be simultaneously bisected by a plane
mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space
Ham_sandwich_theorem
Topics referred to by the same term
the mathematical concept of splitting an object into multiple parts multiplied together Integer factorization, splitting a whole number into the product
Factoring
Poisson manifold that is also a Lie group
g } ( e ) = 0 {\displaystyle \{f,g\}(e)=0} . Applying Weinstein splitting theorem to e {\displaystyle e} one sees that non-trivial Poisson-Lie structure
Poisson–Lie_group
Theorem in group theory
mathematical subject of group theory, the Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality
Grushko_theorem
Relation between genus, degree, and dimension of function spaces over surfaces
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension
Riemann–Roch_theorem
Type of hypersurface
Gregory (2000), "Maximum Principles for Null Hypersurfaces and Null Splitting Theorems", Annales de l'Institut Henri Poincaré A, 1 (3): 543–567, arXiv:math/9909158
Null_hypersurface
Theorem on the number of primes in arithmetic sequences
In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there
Dirichlet's theorem on arithmetic progressions
Dirichlet's_theorem_on_arithmetic_progressions
Theorem in combinatorics generalizing Ramsey's theorem to infinite trees
_{T}\mathbb {S} _{T}^{n}} where T ranges over finitely splitting rooted trees of height ω. Milliken's tree theorem says that not only is S n {\displaystyle \mathbb
Milliken's_tree_theorem
Theorem in topology
functions A. Topological combinatorics Necklace splitting problem Ham sandwich theorem Kakutani's theorem (geometry) Imre Bárány Jha, Aditya; Campbell,
Borsuk–Ulam_theorem
Correspondence between subfields and subgroups
In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions in relation to
Fundamental theorem of Galois theory
Fundamental_theorem_of_Galois_theory
Proof that is not easily verified by hand
computer-assisted proof of the four color theorem, and has since been applied to other arguments, mainly those with excessive case splitting and/or with portions dispatched
Non-surveyable_proof
American mathematician
Together with S.-T. Yau Lawson found basic theorems about these manifolds, such as the Splitting Theorem which says that if the fundamental group splits
H._Blaine_Lawson
Formulae for viscous and incompressible fluid flow at small Reynolds numbers
=\mathbf {u} _{\text{L}}+\mathbf {u} _{\text{T}}} a splitting theorem due to Horace Lamb. The splitting is unique if conditions at infinity (say u = 0 ,
Oseen_equations
Type of product of matrices
row-wise splitting of matrices with a given quantity of rows, was proposed by V. Slyusar in 1996. This matrix operation was named the "face-splitting product"
Khatri–Rao_product
Study of fair cake-cutting with true valuations
n(n-1)^{2}} cuts; this is a corollary of the Stromquist–Woodall theorem and the necklace splitting theorem. In general, an exact division cannot be found by a finite
Truthful_cake-cutting
No-go theorem pertaining the triviality of space-time and internal symmetries
In theoretical physics, the Coleman–Mandula theorem is a no-go theorem stating that spacetime and internal symmetries can only combine in a trivial way
Coleman–Mandula_theorem
Theorem in geometric topology
conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere (the hypersphere that bounds
Poincaré_conjecture
French mathematician (born 1947)
the Mathematics Genealogy Project Sauzin Resurgent functions and splitting theorem , 2007 Boris Sternin, Victor Shatalov Borel-Laplace Transform and
Jean_Écalle
Concerns the decomposition of representations of a finite group into irreducible pieces
In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations
Maschke's_theorem
Mathematical space
As corollary, every compact 3-manifold has a Heegaard splitting. The prime decomposition theorem for 3-manifolds states that every compact, orientable
3-manifold
Election result affecting losing candidate
voting solves the problems of spoilers and vote splitting Morreau, Michael (2014-10-13). "Arrow's Theorem". Stanford Encyclopedia of Philosophy. Retrieved
Spoiler_effect
Extension of recursion theory to admissible ordinals beyond the natural numbers
in other words if every initial portion of A is α-finite. Shore's splitting theorem: Let A be α {\displaystyle \alpha } recursively enumerable and regular
Alpha_recursion_theory
Mathematical game
configuration is a single heap of objects, and the two players take turn splitting a single heap into two heaps of different sizes. The game ends when only
Grundy's_game
equation Quotient rule Ramsey's theorem Rao–Blackwell theorem Rice's theorem Rolle's theorem Splitting lemma squeeze theorem Sum rule in differentiation Sum
List_of_mathematical_proofs
imaginary quadratic fields Stark–Heegner theorem Heegner number Langlands program Different ideal Dedekind domain Splitting of prime ideals in Galois extensions
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
Graph that can be embedded in the plane
conditions hold for v ≥ 3: Theorem 1. e ≤ 3v − 6; Theorem 2. If there are no cycles of length 3, then e ≤ 2v − 4. Theorem 3. f ≤ 2v − 4. In this sense
Planar_graph
Statistical physics theorem
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior
Fluctuation–dissipation theorem
Fluctuation–dissipation_theorem
Concept in differential geometry
Rham decomposition theorem, a principle for splitting a Riemannian manifold into a Cartesian product of Riemannian manifolds by splitting the tangent bundle
Holonomy
Theorem in group theory
The Schur–Zassenhaus theorem is a theorem in group theory which states that if G {\displaystyle G} is a finite group, and N {\displaystyle N} is a normal
Schur–Zassenhaus_theorem
Plurality voting system
theoretically enough to win a majority in the legislature. With enough candidates splitting the vote in a district, the total number of votes needed to win can be
First-past-the-post_voting
Theorem in relativistic quantum mechanics
(2022-09-16). "Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem". Annales Henri Poincaré. 24 (2):
Hegerfeldt's_theorem
Formula of matrix exponentials
in the construction of splitting methods for the numerical solution of differential equations. Moreover, the Lie product theorem is sufficient to prove
Lie_product_formula
Theorem relating Milnor K-theory and Galois cohomology
In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively
Norm residue isomorphism theorem
Norm_residue_isomorphism_theorem
German mathematician (1882–1935)
general theorem, that all maximal subfields of a division algebra D are splitting fields. This paper also contains the Skolem–Noether theorem, which states
Emmy_Noether
Statement in abstract algebra
algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated
Structure theorem for finitely generated modules over a principal ideal domain
Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain
Branch of discrete mathematics
none contains any other? The latter question is answered by Sperner's theorem, which gave rise to much of extremal set theory. The types of questions
Combinatorics
Aspect of algebraic number theory
OL, provides one of the richest parts of algebraic number theory. The splitting of prime ideals in Galois extensions is sometimes attributed to David
Splitting of prime ideals in Galois extensions
Splitting_of_prime_ideals_in_Galois_extensions
Partition result about finite products of infinite trees
In mathematics, the Halpern–Läuchli theorem is a partition result about finite products of infinite trees. Its original purpose was to give a model for
Halpern–Läuchli_theorem
Mathematics textbook
Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry is a graduate-level mathematics textbook in topological combinatorics
Using_the_Borsuk–Ulam_Theorem
Branch of Galois theory in mathematics
{\displaystyle 1\leq i\leq p} , form all the roots—by Fermat's little theorem—so the splitting field is K ( β ) {\displaystyle K(\beta )} . Conversely, any Galois
Artin–Schreier_theory
Mathematical group
fixed. This connection between fields and groups, given by the fundamental theorem of Galois theory, allows for group-theoretic tools to be used on problems
Galois_group
Type of algebraic field extension
extension. For finite extensions, a normal extension is identical to a splitting field. Let L / K {\displaystyle L/K} be an algebraic extension (i.e.,
Normal_extension
American mathematician (born 1953)
Journal of combinatorial theory. Series B, 1983. Erdős–Gallai theorem Necklace splitting problem Douglas Brent West at the Mathematics Genealogy Project
Douglas_West_(mathematician)
Version without requiring the smooth manifolds involved to carry a complex structure
are just the Thom isomorphism. Then, using the splitting principle, it suffices to check the theorem via explicit computation for line bundles. If f:
Riemann–Roch theorem for smooth manifolds
Riemann–Roch_theorem_for_smooth_manifolds
Algebraic field extension
extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory. A result of Emil Artin allows one to construct Galois
Galois_extension
Theorem about fixed points of multiple variables
In computability theory, Bekić's theorem or Bekić's lemma is a theorem about fixed-points which allows splitting a mutual recursion into recursions on
Bekić's_theorem
Integral expressing the amount of overlap of one function as it is shifted over another
case f∗g is also integrable (Stein & Weiss 1971, Theorem 1.3). This is a consequence of Tonelli's theorem. This is also true for functions in L1, under the
Convolution
Mathematical concept
equivalent to Definition A when the underlying measure space is finite (see Theorem 2 below), Definition H is widely adopted in Mathematics. The following
Uniform_integrability
Pole splitting is a phenomenon exploited in some forms of frequency compensation used in an electronic amplifier. When a capacitor is introduced between
Pole_splitting
On when a definite intersection form of a smooth 4-manifold is diagonalizable
mathematics, and especially differential topology and gauge theory, Donaldson's theorem states that a definite intersection form of a closed, oriented, smooth
Donaldson's_theorem
Algebraic topology uses abstract algebra to study topological spaces
Applications Jordan curve theorem Brouwer fixed point theorem Invariance of domain Lefschetz fixed-point theorem Hairy ball theorem Degree of a continuous
List of algebraic topology topics
List_of_algebraic_topology_topics
Euclidean 3-manifolds, Bieberbach Theorem, Flat manifolds, Crystallographic groups Seifert fiber space Heegaard splitting Waldhausen conjecture Compression
List of geometric topology topics
List_of_geometric_topology_topics
French mathematician (1923–2002)
stratified isotopy theorem describing the local conical structure of Whitney stratified sets, now known as the Thom–Mather isotopy theorem. Much of his work
René_Thom
Part of the mathematical subject of group theory
generalized accessibility theorem stating that for any finitely presented group G there is a bound on the complexity of reduced splittings of G over small subgroups
Bass–Serre_theory
Integration over a non-flat region in 3D space
and vector calculus, such as the divergence theorem, magnetic flux, and its generalization, Stokes' theorem. Let us notice that we defined the surface
Surface_integral
Property of a circuit
circuit that relates voltages and currents at two points. The reciprocity theorem states that the current at one point in a circuit due to a voltage at a
Reciprocity (electrical networks)
Reciprocity_(electrical_networks)
Type of fair division
Consensus splitting, also called exact division, is a partition of a continuous resource ("cake") into some k pieces, such that each of n people with
Consensus_splitting
travel, tourism, insurance
SPLITTING THEOREM
SPLITTING THEOREM
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SPLITTING THEOREM
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SPLITTING THEOREM
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travel, tourism, insurance