## Proceedings of the Centre for Mathematics and its Applications

### Spectral flow in Breuer-Fredholm modules

#### Abstract

This review discusses work in progress and related earlier studies by many authors. We have attempted to place our results in their broadcontext beginning with the $L^2$ index theorem of Atiyah and Singer, subsequent extensions and the motivation for our results and conjectures. The geometric setting is the analysis of $L^2$ invariants of non-compact covering spaces, several of which are not present (or are trivial) on compact mamfolds. These invariants use the von Neumann algebra of the covering transformation group in an essential way.

#### Article information

Dates
First available in Project Euclid: 18 November 2014