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What is the role of equivariance in the Atiyah-Singer index theorem?

I think that some modest bit of equivariant K-theory is required in the K-theory proof of the index theorem. … I suppose Atiyah and Singer found a way to work in $O(n)$-equivariant K-theory instead, but then again they weren't even using the language of K-homology. …
Paul Siegel's user avatar
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