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Groups of fast homeomorphisms of the interval and the ping-pong argument
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dc.contributor.author | Bleak, Collin | |
dc.contributor.author | Brin, Matthew G. | |
dc.contributor.author | Kassabov, Martin | |
dc.contributor.author | Tatch Moore, Justin | |
dc.contributor.author | Zaremsky, Matthew C. B. | |
dc.date.accessioned | 2019-10-02T15:30:03Z | |
dc.date.available | 2019-10-02T15:30:03Z | |
dc.date.issued | 2019-01-31 | |
dc.identifier.citation | Bleak , 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/25 | en |
dc.identifier.issn | 2415-6302 | |
dc.identifier.other | PURE: 252044171 | |
dc.identifier.other | PURE UUID: 8e3d1095-1209-42ab-9bcc-5a501534d357 | |
dc.identifier.other | WOS: 000457558900001 | |
dc.identifier.other | Scopus: 85069666291 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/73701278 | |
dc.identifier.uri | https://hdl.handle.net/10023/18600 | |
dc.description.abstract | We 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.iso | eng | |
dc.relation.ispartof | Journal of Combinatorial Algebra | en |
dc.rights | Copyright © 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/25 | en |
dc.subject | Algebraically fast | en |
dc.subject | Dynamical diagram | en |
dc.subject | Free group | en |
dc.subject | Geometrically fast | en |
dc.subject | Geometrically proper | en |
dc.subject | Homeomorphism group | en |
dc.subject | Piecewise linear | en |
dc.subject | Ping-Pong lemma | en |
dc.subject | Symbol space | en |
dc.subject | Symbolic dynamics | en |
dc.subject | Thompson's group | en |
dc.subject | Transition chain | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.title | Groups of fast homeomorphisms of the interval and the ping-pong argument | en |
dc.type | Journal article | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.4171/JCA/25 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1701.08321 | en |
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