Atiyah's $L^2$-Index theorem

Details Atiyah's $L^2$-Index theorem Atiyah's $L^2$-Index theorem

2010-04-08

arxiv.org/abs/1004.1350v1

L'enseignement Math\'ematique 49 (2003), 85 - 93.

Mathematics

K-Theory and Homology

7 pages

Scientific paper

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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