An irrational-slope Thompson’s group
- 1 July 2021
- journal article
- research article
- Published by Universitat Autonoma de Barcelona in Publicacions Matemàtiques
- Vol. 65 (2), 809-839
- https://doi.org/10.5565/publmat6522112
Abstract
The purpose of this paper is to study the properties of the irrational-slope Thompson's group F-tau introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson's group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary, we see that several embeddings of F in F-tau are undistorted.Keywords
This publication has 2 references indexed in Scilit:
- Coherent actions by homeomorphisms on the real line or an intervalIsrael Journal of Mathematics, 2019
- Growth of Positive Words in Thompson's GroupFCommunications in Algebra, 2004