mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology...
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Lev Semyonovich Pontryagin (Russian: Лев Семёнович Понтрягин, also written Pontriagin or Pontrjagin, first name sometimes anglicized as Leon) (3 September...
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In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which...
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Thom isomorphism Generalized Gauss–Bonnet theorem Chern class Pontryagin class Stiefel-Whitney class Bott, Raoul and Tu, Loring W. (1982). Differential Forms...
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fundamental characteristic classes known at that time (the Stiefel–Whitney class, the Chern class, and the Pontryagin classes) were reflections of the classical...
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manifolds have a well-defined Chern class. (See Arakelov geometry) Pontryagin class Stiefel–Whitney class Euler class Segre class Schubert calculus Quantum Hall...
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Thom space (redirect from Pontryagin-Thom construction)
mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential...
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(The variables p k {\displaystyle p_{k}} will often in practice be Pontryagin classes.) The genus Φ {\displaystyle \Phi } of compact, connected, smooth...
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Obstruction theory Characteristic class Chern class Chern–Simons form Pontryagin class Pontryagin number Stiefel–Whitney class Poincaré conjecture Cohomology...
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homomorphism Chern class Chern–Simons form Chern–Simons theory Chern's conjecture (affine geometry) Pontryagin number Pontryagin class De Rham cohomology...
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paper proved the existence of rational Pontryagin classes on topological manifolds. The rational Pontryagin classes are essential ingredients of the index...
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Cohomology (redirect from Cohomology class)
characteristic classes for vector bundles that take values in cohomology, including Chern classes, Stiefel–Whitney classes, and Pontryagin classes. For each...
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or OEIS: A237111). By taking for the p i {\displaystyle p_{i}} the Pontryagin classes p i ( M ) {\displaystyle p_{i}(M)} of the tangent bundle of a 4n dimensional...
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In mathematics, a Pontryagin cohomology operation is a cohomology operation taking cohomology classes in H2n(X,Z/prZ) to H2pn(X,Z/pr+1Z) for some prime...
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Gelfand–Kirillov dimension; integral geometry; combinatorial definition of the Pontryagin class; Coxeter functors; general hypergeometric functions; Gelfand–Tsetlin...
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{\displaystyle G_{2}} has finite fundamental group, non-zero first Pontryagin class, and non-zero third and fourth Betti numbers. The fact that G 2 {\displaystyle...
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conjecture concerns the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group. According to the...
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manifold. This associates to any spin manifold with vanishing half first Pontryagin class a modular form. By work of Hopkins, Matthew Ando, Charles Rezk and...
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one of the Pontryagin classes, in real four-dimensional cohomology. In this way foundational cases for the theory of characteristic classes depend only...
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manifolds; and various characteristic classes, such as Euler characteristic, the Hirzebruch signature (Pontryagin class), the Rarita–Schwinger index (spin-3/2...
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Characteristic class for a general survey, in particular Chern class, the direct analogue for complex vector bundles Real projective space Pontryagin, Lev S....
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of characteristic classes of principal bundles (Chern–Weil theory), it covers Euler classes, Chern classes, and Pontryagin classes. The second volume...
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bundles of the rest have nontrivial Stiefel–Whitney and Pontryagin classes. The total classes are given by the following formulas: w ( H P n ) = ( 1 +...
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most well-known being his proof of the topological invariance of the Pontryagin classes of the differentiable manifold. His work included a study of the cohomology...
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signature operator are homotopy-invariant. Hirzebruch signature theorem Pontryagin class Friedrich Hirzebruch Michael Atiyah Isadore Singer Atiyah & Bott 1967...
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of classifying spaces BG; of characteristic classes such as the Stiefel-Whitney class and Pontryagin class. 1945 Samuel Eilenberg and Norman Steenrod Eilenberg–Steenrod...
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Structurally stable systems were introduced by Aleksandr Andronov and Lev Pontryagin in 1937 under the name "systèmes grossiers", or rough systems. They announced...
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(declined both) Lev Pontryagin, blind mathematician, developed Pontryagin duality and Pontryagin classes in topology, and Pontryagin's minimum principle...
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and Wolfgang Krull's theory of their Galois groups. This combined with Pontryagin duality to give a clearer if more abstract formulation of the central...
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high-dimensional manifolds. He proved the topological invariance of the rational Pontryagin classes, and posed the Novikov conjecture. From about 1971, he moved to work...
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