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

Jeroen Schillewaert; Matthew J. Conder

arxiv: 2103.15257 · v2 · pith:TI3DC7YX · submitted 2021-03-29 · math.GR · math.GT· math.MG

A strong Schottky lemma on n generators for CAT(0) spaces

Matthew J. Conder , Jeroen Schillewaert This is my paper

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keywords generatorsgroupmathrmadditionalalperinanglesassumptioncompact

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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.

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A strong Schottky lemma on n generators for CAT(0) spaces

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