Thomas Schick: L2-index Theorem for Boundary-Manifolds
Suppose M is a compact manifold with boundary N. Let
\tilde M over M be a normal covering with covering group
Gamma. Suppose (A,T) is an elliptic differential boundary value
problem on M with lift (\tilde A,\tilde T) to \tilde 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, equals the index of
(A,T).
In this way, we extend the
classical L^2-index
theorem of Atiyah to manifolds with boundary.
Thomas
Schick