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

  • Collin Bleak

    University of St Andrews, UK
  • Matthew G. Brin

    Binghamton University, USA
  • Martin Kassabov

    Cornell University, Ithaca, USA
  • Justin Tatch Moore

    Cornell University, Ithaca, USA
  • Matthew C.B. Zaremsky

    University of Albany (SUNY), USA
Groups of fast homeomorphisms of the interval and the ping-pong argument cover

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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 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 into Richard Thompson’s group . In particular, every member of our class of generating sets generates a group which embeds into and in particular is not a free product. An analogous abstract theory is also developed for groups of permutations of an infinite set.

Cite this article

Collin Bleak, Matthew G. Brin, Martin Kassabov, Justin Tatch Moore, Matthew C.B. Zaremsky, Groups of fast homeomorphisms of the interval and the ping-pong argument. J. Comb. Algebra 3 (2019), no. 1, pp. 1–40

DOI 10.4171/JCA/25