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Results tagged with characteristic-classes
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user 4991
Cohomology classes associated to vector bundles. Includes Stiefel-Whitney classes, Chern classes, Pontryagin classes, and the Euler class.
12
votes
Construction of the Stiefel-Whitney and Chern Classes
Let me offer another definition not far from obstruction theory (as Ilya gave), but without referring to obstruction theory and thus more elementary.
Suppose for simplicity that $X$ is a simplicial c …
- 4,990
4
votes
Natural setting for characteristic classes?
[I tried to make this a comment, but ran out of space...]
I'm not 100% clear on your question, but do see some possible answer(s).
The homotopical generalization of a manifold is a Poincare duality …
- 4,990
3
votes
Which sets of Stiefel-Whitney characteristic numbers can be realized as coming from a manifold?
Recall Thom's result that cobordism groups are homotopy groups of Thom spaces/ spectra. The characteristic numbers of $[M]$ are encoding the image of the corresponding element of $\pi_* MO$ under t …
- 4,990
24
votes
Intuitive explanation for the Atiyah-Singer index theorem
I am going to give a topologically biased answer, which will proceed by restating what the Index Theorem says so that its plausibility (though not its truth) is more immediate. [Oops - I see that Pau …
- 4,990