L²-index theorem for elliptic differential boundary problems

Thomas Schick

Vol. 197 (2001), No. 2, 423–439

DOI: 10.2140/pjm.2001.197.423

Abstract

Suppose M is a compact manifold with boundary ∂M. Let M be a normal covering of M. Suppose (A,T) is an elliptic differential boundary value problem on M with lift (Ã,T) to M. 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 of (Ã,T), equals the index of (A,T). In this way, we extend the classical L²-index theorem of Atiyah to elliptic differential boundary value problems.

Milestones

Received: 2 February 1999

Published: 1 February 2001