mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology...

Lev Semyonovich Pontryagin (Russian: Лев Семёнович Понтрягин, also written Pontriagin or Pontrjagin, first name sometimes anglicized as Leon) (3 September...

In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which...

Thom isomorphism Generalized Gauss–Bonnet theorem Chern class Pontryagin class Stiefel-Whitney class Bott, Raoul and Tu, Loring W. (1982). Differential Forms...

fundamental characteristic classes known at that time (the Stiefel–Whitney class, the Chern class, and the Pontryagin classes) were reflections of the classical...

manifolds have a well-defined Chern class. (See Arakelov geometry) Pontryagin class Stiefel–Whitney class Euler class Segre class Schubert calculus Quantum Hall...

mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential...

(The variables p k {\displaystyle p_{k}} will often in practice be Pontryagin classes.) The genus Φ {\displaystyle \Phi } of compact, connected, smooth...

Obstruction theory Characteristic class Chern class Chern–Simons form Pontryagin class Pontryagin number Stiefel–Whitney class Poincaré conjecture Cohomology...

homomorphism Chern class Chern–Simons form Chern–Simons theory Chern's conjecture (affine geometry) Pontryagin number Pontryagin class De Rham cohomology...

paper proved the existence of rational Pontryagin classes on topological manifolds. The rational Pontryagin classes are essential ingredients of the index...

characteristic classes for vector bundles that take values in cohomology, including Chern classes, Stiefel–Whitney classes, and Pontryagin classes. For each...

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...

Gelfand–Kirillov dimension; integral geometry; combinatorial definition of the Pontryagin class; Coxeter functors; general hypergeometric functions; Gelfand–Tsetlin...

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...

{\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...

conjecture concerns the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group. According to the...

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...

one of the Pontryagin classes, in real four-dimensional cohomology. In this way foundational cases for the theory of characteristic classes depend only...

manifolds; and various characteristic classes, such as Euler characteristic, the Hirzebruch signature (Pontryagin class), the Rarita–Schwinger index (spin-3/2...

Characteristic class for a general survey, in particular Chern class, the direct analogue for complex vector bundles Real projective space Pontryagin, Lev S....

of characteristic classes of principal bundles (Chern–Weil theory), it covers Euler classes, Chern classes, and Pontryagin classes. The second volume...

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 +...

signature operator are homotopy-invariant. Hirzebruch signature theorem Pontryagin class Friedrich Hirzebruch Michael Atiyah Isadore Singer Atiyah & Bott 1967...

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...

of classifying spaces BG; of characteristic classes such as the Stiefel-Whitney class and Pontryagin class. 1945 Samuel Eilenberg and Norman Steenrod Eilenberg–Steenrod...

Structurally stable systems were introduced by Aleksandr Andronov and Lev Pontryagin in 1937 under the name "systèmes grossiers", or rough systems. They announced...

(declined both) Lev Pontryagin, blind mathematician, developed Pontryagin duality and Pontryagin classes in topology, and Pontryagin's minimum principle...

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...

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...