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.

Authors