Volume 13, issue 6 (2013)

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Abels's groups revisited

Stefan Witzel

Algebraic & Geometric Topology 13 (2013) 3447–3467
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 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/