Free products in R. Thompson’s group V

C Bleak, O Salazar-Diaz

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
5 Downloads (Pure)

Abstract

We investigate some product structures in R. Thompson's group V, primarily by studying the topological dynamics associated with V's action on the Cantor set C. We draw attention to the class D(V,C) of groups which have embeddings as demonstrative subgroups of V whose class can be used to assist in forming various products. Note that D(V,C) contains all finite groups, the free group on two generators, and Q/Z, and is closed under passing to subgroups and under taking direct products of any member by any finite member. If G≤V and H ∈ D(V,C), then G~H embeds into V. Finally, if G, H ∈ D(V,C), then G*H embeds in V.
Using a dynamical approach, we also show the perhaps surprising result that Z2 * Z does not embed in V, even though V has many embedded copies of Z2 and has many embedded copies of free products of various pairs of its subgroups.

Original languageEnglish
Pages (from-to)5967-5997
Number of pages31
JournalTransactions of the American Mathematical Society
Volume365
Issue number11
Early online date19 Jun 2013
DOIs
Publication statusPublished - 1 Nov 2013

Keywords

  • R. Thompson Groups
  • Homeomorphisms
  • Cantor set

Fingerprint

Dive into the research topics of 'Free products in R. Thompson’s group V'. Together they form a unique fingerprint.

Cite this