%0 Journal Article
%T Atiyah's $L^2$-Index theorem
%A Indira Chatterji
%A Guido Mislin
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1004.1350v1