Groups of fast homeomorphisms of the interval and the ping-pong argument

Collin Bleak, Matthew G. Brin, Martin Kassabov, Justin Tatch Moore, Matthew C. B. Zaremsky

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6 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)1-40
JournalJournal of Combinatorial Algebra
Volume3
Issue number1
DOIs
Publication statusPublished - 31 Jan 2019

Keywords

  • Algebraically fast
  • Dynamical diagram
  • Free group
  • Geometrically fast
  • Geometrically proper
  • Homeomorphism group
  • Piecewise linear
  • Ping-Pong lemma
  • Symbol space
  • Symbolic dynamics
  • Thompson's group
  • Transition chain

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