Groups of fast homeomorphisms of the interval and the ping-pong argument
type: Item
instance of: scholarly article
title: Groups of fast homeomorphisms of the interval and the ping-pong argument
DOI: 10.4171/JCA/25
author: Collin Bleak
author: Matthew G. Brin
author: Martin Kassabov
author: Justin Tatch Moore
author: Matthew C. B. Zaremsky
published in: Journal of Combinatorial Algebra
publication date: 2019-04-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1701.08321
review text: Summary: 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.
Mathematics Subject Classification ID: 20B07
Mathematics Subject Classification ID: 20B10
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 7047429
zbMATH Keywords: algebraically fast
zbMATH Keywords: dynamical diagram
zbMATH Keywords: free group
zbMATH Keywords: geometrically fast
zbMATH Keywords: geometrically proper
zbMATH Keywords: homeomorphism group
zbMATH Keywords: piecewise linear
zbMATH Keywords: ping-pong lemma
zbMATH Keywords: symbol space
zbMATH Keywords: symbolic dynamics
zbMATH Keywords: Thompson's group
zbMATH Keywords: transition chain
MaRDI profile type: Publication
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Wikidata QID: Q128467742
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description: scientific article; zbMATH DE number 7047429