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Cohomology classes associated to vector bundles. Includes Stiefel-Whitney classes, Chern classes, Pontryagin classes, and the Euler class.

18 votes

How we do actually compute the topological index in Atiyah-Singer?

This isn't really going to be an answer, but it's too long to be a comment and I think it will be helpful. First, as the other answerers pointed out it is a good idea to avoid boundary value problems …
Paul Siegel's user avatar
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42 votes
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Intuitive explanation for the Atiyah-Singer index theorem

I don't think I can really give you the intuition that you seek because I don't think I quite have it yet either. But I think that understanding the relevance of Nigel Higson's comment might help, an …
Paul Siegel's user avatar
  • 29.2k