Volume 10 (2007)

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Homotopy idempotents on manifolds and Bass' conjectures

A J Berrick, I Chatterji and G Mislin

Geometry & Topology Monographs 10 (2007) 41–62

DOI: 10.2140/gtm.2007.10.41

arXiv: 0903.4341

Abstract

The Bass trace conjectures are placed in the setting of homotopy idempotent selfmaps of manifolds. For the strong conjecture, this is achieved via a formulation of Geoghegan. The weaker form of the conjecture is reformulated as a comparison of ordinary and L2–Lefschetz numbers.

Keywords

Bass Conjecture, homotopy idempotent, fixed point, Nielsen number, Reidemeister trace, Wall finiteness obstruction, L²–Betti number, L²–Lefschetz number, L²–Euler characteristic

Mathematical Subject Classification

Primary: 19A31, 54H25, 55M20, 58C30

Secondary: 46L10, 57N50

References
Publication

Received: 4 October 2004
Revised: 2 April 2005
Published: 29 January 2007

Authors
A J Berrick
Department of Mathematics
National University of Singapore
Kent Ridge 117543
Singapore
I Chatterji
Department of Mathematics
The Ohio State University
231 W 18th Ave
Columbus OH 43210
USA
G Mislin
Department of Mathematics
ETH Zürich
8092 Zürich
Switzerland