#### 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.

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