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arXiv · 1004.1350

Atiyah's $L^2$-Index theorem

Indira Chatterji·Guido Mislin
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Abstract

The $L^2$-Index Theorem of Atiyah \cite{atiyah} expresses the index of an elliptic operator on a closed manifold $M$ in terms of the $G$-equivariant index of some regular covering $\widetilde{M}$ of $M$, with $G$ the group of covering transformations. Atiyah's proof is analytic in nature. Our proof is algebraic and involves an embedding of a given group into an acyclic one, together with naturality properties of the indices.

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Indira Chatterji, Guido Mislin. 2010-04-08. Atiyah's $L^2$-Index theorem. https://arxiv.org/abs/1004.1350

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