L2-index theorem for manifolds with boundary

Details L2-index theorem for manifolds with boundary L2-index theorem for manifolds with boundary

1998-10-21

arxiv.org/abs/math/9810133v1

Pacific J. Math. {\bf 197} (2001), no.~2, 423--439; MR 2001m:58053

Mathematics

Geometric Topology

AMS-LaTeX2e, 19 pages

Scientific paper

Suppose M is a compact manifold with boundary. Let N be a normal covering of M. Suppose (A,T) is an elliptic differential boundary value problem on M with lift (\tilde A,\tilde T) to N. Then the von Neumann dimension of kernel and cokernel of this lift are defined. The main result of this paper is: these numbers are finite, and their difference, by definition the von Neumann index, equals the index of (A,T). In this way, we extend the classical L^2-index theorem of Atiyah to manifolds with boundary.

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