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What is the role of equivariance in the Atiyah-Singer index theorem?
structure of the proof:
Define (using purely K-theoretic means) a homomorphism $K_G(TX) \to R(G)$ where $G$ is a compact Lie group, $X$ a $G$-manifold, $R(G)$ the representation ring, and $K_G(TX)$ the equivariant … Let's say hypothetically that I'm a non-equivariant person and only care about plain differential operators on plain manifolds. …