Abels’s groups revisited

Witzel, Stefan

doi:10.2140/agt.2013.13.3447

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Abels's groups revisited

Stefan Witzel

Algebraic & Geometric Topology 13 (2013) 3447–3467

DOI: 10.2140/agt.2013.13.3447

Abstract

We generalize a class of groups introduced by Herbert Abels to produce examples of virtually torsion free groups that have Bredon-finiteness length $m - 1$ and classical finiteness length $n - 1$ for all $0 < m \leq n$ .

The proof illustrates how Bredon-finiteness properties can be verified using geometric methods and a version of Brown’s criterion due to Martin Fluch and the author.

Keywords

finiteness properties, Bredon homology, Abels's groups, horospheres, arithmetic groups, buildings

Mathematical Subject Classification 2010

Primary: 20J05, 22E40

Secondary: 51E24, 57M07

References

Publication

Received: 8 October 2012

Accepted: 27 February 2013

Published: 10 October 2013

Authors

Stefan Witzel
Mathematisches Institut Westfälische Wilhelms-Universtität Münster Einsteinstraße 62 48149 Münster Germany
http://www.math.uni-muenster.de/u/stefan.witzel/

Volume 13, issue 6 (2013)