Algebraic & Geometric Topology

Abels's groups revisited

Stefan Witzel

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We generalize a class of groups introduced by Herbert Abels to produce examples of virtually torsion free groups that have Bredon-finiteness length m1 and classical finiteness length n1 for all 0<mn.

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.

Article information

Algebr. Geom. Topol., Volume 13, Number 6 (2013), 3447-3467.

Received: 8 October 2012
Accepted: 27 February 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20J05: Homological methods in group theory 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 51E24: Buildings and the geometry of diagrams 57M07: Topological methods in group theory

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


Witzel, Stefan. Abels's groups revisited. Algebr. Geom. Topol. 13 (2013), no. 6, 3447--3467. doi:10.2140/agt.2013.13.3447.

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