Product on the homology of a topological space induced by a product on the topological space
In mathematics, the Pontryagin product, introduced by Lev Pontryagin (1939), is a product on the homology of a topological space induced by a product on the topological space. Special cases include the Pontryagin product on the homology of an abelian group, the Pontryagin product on an H-space, and the Pontryagin product on a loop space.
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mathematics, the Pontryaginproduct, introduced by Lev Pontryagin (1939), is a product on the homology of a topological space induced by a product on the topological...
mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in...
In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which...
\rangle ,J)} is called a Pontryagin space or Π κ {\displaystyle \Pi _{\kappa }} -space. (Conventionally, the indefinite inner product is given the sign that...
mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential...
Arkhangel'skii and L. S. Pontryagin (Eds.), Springer-Verlag, Berlin ISBN 3-540-18178-4. V. V. Filippov, On the inductive dimension of the product of bicompacta,...
{\displaystyle [\mathrm {id} _{S^{2}},\mathrm {id} _{S^{2}}]} . Using the Pontryagin–Thom construction there is a direct geometric argument, using the fact...
Obstruction theory Characteristic class Chern class Chern–Simons form Pontryagin class Pontryagin number Stiefel–Whitney class Poincaré conjecture Cohomology operation...
of characteristic numbers are Stiefel–Whitney numbers, Chern numbers, Pontryagin numbers, and the Euler characteristic. Given an oriented manifold M of...
boundary operator, chain complexes J. W. Alexander, Solomon Lefschetz, Lev Pontryagin, Andrey Kolmogorov, Norman Steenrod, Eduard Čech: the early cochain notions...
be stated more simply in terms of cohomology. In 1934, Lev Pontryagin proved the Pontryagin duality theorem; a result on topological groups. This (in rather...
it is a projective limit of tori (products of a finite number of copies of the circle group), or the Pontryagin dual of a discrete torsion-free abelian...
{Q} _{p}} is also self-dual.) It follows that the adeles are self-dual. Pontryagin duality asserts that the functor G ↦ G ^ {\displaystyle G\mapsto {\hat...
d ( E ) ∈ H 2 d ( X ) {\displaystyle e(E)=c_{d}(E)\in H^{2d}(X)} The Pontryagin class p r ( E ) {\displaystyle p_{r}(E)} is defined as the Chern class...
Hausdorff abelian group, and thus its Pontryagin dual must be a discrete abelian group. In fact, the Pontryagin dual of Z ^ {\displaystyle {\widehat {\mathbb...
Parseval's formula, or Parseval's relation, or even Parseval's theorem. See Pontryagin duality for a general formulation of this concept in the context of locally...
representation theory for locally compact abelian groups is described by Pontryagin duality. Any compact group is locally compact. In particular the circle...
equivalent to the opposite of the category of commutative rings. The Pontryagin duality restricts to an equivalence between the category of compact Hausdorff...
(declined both) Lev Pontryagin, blind mathematician, developed Pontryagin duality and Pontryagin classes in topology, and Pontryagin's minimum principle...
Mathematically, the duality between position and momentum is an example of Pontryagin duality. In particular, if a function is given in position space, f(r)...
the concept of an injective cogenerator is drawn from examples such as Pontryagin duality. Generators are objects which cover other objects as an approximation...
{\hat {G}}} is a group, in fact another locally compact abelian group. Pontryagin duality states that for a locally compact abelian group G, the dual of...
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