English

L2-index theorem for manifolds with boundary

Geometric Topology 2018-11-28 v1

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.

Keywords

Cite

@article{arxiv.math/9810133,
  title  = {L2-index theorem for manifolds with boundary},
  author = {Thomas Schick},
  journal= {arXiv preprint arXiv:math/9810133},
  year   = {2018}
}

Comments

AMS-LaTeX2e, 19 pages

R2 v1 2026-07-22T18:00:34.135Z