A strong Schottky lemma on $n$ generators for $\mathrm{CAT}(0)$ spaces

Matthew J. Conder; Jeroen Schillewaert

A strong Schottky lemma on $n$ generators for $\mathrm{CAT}(0)$ spaces

Group Theory 2022-01-25 v2 Geometric Topology Metric Geometry

Authors: Matthew J. Conder , Jeroen Schillewaert

Abstract

We give a criterion for a set of $n$ hyperbolic isometries of a $\mathrm{CAT}(0)$ metric space $X$ to generate a free group on $n$ generators. This extends a result by Alperin, Farb and Noskov who proved this for 2 generators under the additional assumption that $X$ is complete and has no fake zero angles. Moreover, when $X$ is locally compact, the group we obtain is also discrete.

Keywords

group theory hyperbolic groups topological groups

Cite

@article{arxiv.2103.15257,
  title  = {A strong Schottky lemma on $n$ generators for $\mathrm{CAT}(0)$ spaces},
  author = {Matthew J. Conder and Jeroen Schillewaert},
  journal= {arXiv preprint arXiv:2103.15257},
  year   = {2022}
}

Comments

7 pages, final version to appear in M\"unst. J. Math

A strong Schottky lemma on $n$ generators for $\mathrm{CAT}(0)$ spaces

Abstract

Keywords

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