Hyperbolic groups have flat-rank at most 1

Details Hyperbolic groups have flat-rank at most 1 Hyperbolic groups have flat-rank at most 1

2009-11-23

arxiv.org/abs/0911.4461v1

Mathematics

Group Theory

19 pages, submitted

Scientific paper

The flat-rank of a totally disconnected, locally compact group G is an integer, which is an invariant of G as a topological group. We generalize the concept of hyperbolic groups to the topological context and show that a totally disconnected, locally compact, hyperbolic group has flat-rank at most 1. It follows that the simple totally disconnected locally compact groups constructed by Paulin and Haglund have flat-rank at most 1.

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