Hyperbolic groups have flat-rank at most 1

Udo Baumgartner; Rögnvaldur G. Möller; George A. Willis

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arXiv · 0911.4461

Hyperbolic groups have flat-rank at most 1

Udo Baumgartner·Rögnvaldur G. Möller·George A. Willis

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Abstract

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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Udo Baumgartner, Rögnvaldur G. Möller, George A. Willis. 2009-11-23. Hyperbolic groups have flat-rank at most 1. https://arxiv.org/abs/0911.4461

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