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dc.contributor.authorBleak, Collin
dc.contributor.authorBrin, Matthew G.
dc.contributor.authorKassabov, Martin
dc.contributor.authorTatch Moore, Justin
dc.contributor.authorZaremsky, Matthew C. B.
dc.date.accessioned2019-10-02T15:30:03Z
dc.date.available2019-10-02T15:30:03Z
dc.date.issued2019-01-31
dc.identifier.citationBleak , C , Brin , M G , Kassabov , M , Tatch Moore , J & Zaremsky , M C B 2019 , ' Groups of fast homeomorphisms of the interval and the ping-pong argument ' , Journal of Combinatorial Algebra , vol. 3 , no. 1 , pp. 1-40 . https://doi.org/10.4171/JCA/25en
dc.identifier.issn2415-6302
dc.identifier.otherPURE: 252044171
dc.identifier.otherPURE UUID: 8e3d1095-1209-42ab-9bcc-5a501534d357
dc.identifier.otherWOS: 000457558900001
dc.identifier.otherScopus: 85069666291
dc.identifier.otherORCID: /0000-0001-5790-1940/work/73701278
dc.identifier.urihttp://hdl.handle.net/10023/18600
dc.description.abstractWe adapt the Ping-Pong lemma, which historically was used to study free products of groups, to the setting of the homeomorphism group of the unit interval. As a consequence, we isolate a large class of generating sets for subgroups of Homeo+(I) for which certain finite dynamical data can be used to determine the marked isomorphism type of the groups which they generate. As a corollary, we will obtain a criterion for embedding subgroups of Homeo+(I) into Richard Thompson’s group F . In particular, every member of our class of generating sets generates a group which embeds into F and in particular is not a free product. An analogous abstract theory is also developed for groups of permutations of an infinite set.
dc.language.isoeng
dc.relation.ispartofJournal of Combinatorial Algebraen
dc.rightsCopyright © 2019 EMS Publishing House. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.4171/JCA/25en
dc.subjectAlgebraically fasten
dc.subjectDynamical diagramen
dc.subjectFree groupen
dc.subjectGeometrically fasten
dc.subjectGeometrically properen
dc.subjectHomeomorphism groupen
dc.subjectPiecewise linearen
dc.subjectPing-Pong lemmaen
dc.subjectSymbol spaceen
dc.subjectSymbolic dynamicsen
dc.subjectThompson's groupen
dc.subjectTransition chainen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subjectR2Cen
dc.subject.lccQAen
dc.titleGroups of fast homeomorphisms of the interval and the ping-pong argumenten
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.4171/JCA/25
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/1701.08321en


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