Proceedings of the Centre for Mathematics and its Applications

Spectral flow in Breuer-Fredholm modules

A.L. Carey and John Phillips

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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

Source
Joint Australian-Taiwanese Workshop on Analysis and Applications. Tim Cranny and Bevan Thompson, eds. Proceedings of the Centre for Mathematics and its Applications, v. 37. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1999), 99-108

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416323129

Citation

Carey, A.L.; Phillips, John. Spectral flow in Breuer-Fredholm modules. Joint Australian-Taiwanese Workshop on Analysis and Applications, 99--108, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1999.https://projecteuclid.org/euclid.pcma/1416323129


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