L2-index theorem for manifolds with boundary

Thomas Schick

doi:10.2140/pjm.2001.197.423

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L2-index theorem for manifolds with boundary

Thomas Schick

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Abstract

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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Thomas Schick. 1998-10-21. L2-index theorem for manifolds with boundary. https://doi.org/10.2140/pjm.2001.197.423

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