Groups of fast homeomorphisms of the interval and the ping-pong argument
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.
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
Publication
Journal of Combinatorial Algebra
Status
Peer reviewed
ISSN
2415-6302Type
Journal article
Rights
Copyright © 2019 EMS Publishing House. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.4171/JCA/25
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.