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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 | 252044171 | |
dc.identifier | 8e3d1095-1209-42ab-9bcc-5a501534d357 | |
dc.identifier | 000457558900001 | |
dc.identifier | 85069666291 | |
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 | 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.format.extent | 445556 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Combinatorial Algebra | 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.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 | 10.4171/JCA/25 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1701.08321 | en |
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