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

 dc.contributor.author Conder, Matthew J dc.contributor.author Schillewaert, Jeroen dc.date.accessioned 2022-05-03T02:35:04Z dc.date.available 2022-05-03T02:35:04Z dc.date.issued 2021-3-29 dc.identifier.citation Arxiv, 29 Mar 2021 dc.identifier.uri https://hdl.handle.net/2292/58869 dc.description.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. dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.subject math.GR dc.subject math.GR dc.subject math.GT dc.subject math.MG dc.subject 20F65 dc.title A strong Schottky lemma on $n$ generators for $\mathrm{CAT}(0)$ spaces dc.type Journal Article dc.date.updated 2022-04-04T02:01:03Z dc.rights.holder Copyright: The author en pubs.author-url http://arxiv.org/abs/2103.15257v2 dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en pubs.elements-id 845484
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