An irrational-slope Thompson’s group

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 2021Embargo end date: 01 Jan 2018 Australia, Spain English Publisher:Universitat Autonoma de BarcelonaJournal:Publicacions Matemàtiques, volume 65, pages 809-839 (issn: 0214-1493,

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Authors: José Burillo; Brita Nucinkis; Lawrence Reeves;

doi: 10.5565/publmat6522112 , 10.48550/arxiv.1806.00108

arXiv: 1806.00108

handle: 2117/365461 , 11343/309675

An irrational-slope Thompson’s group

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Abstract

The purpose of this paper is to study the properties of the irrational-slope Thompson's group $F_τ$ introduced by Cleary in 1995. 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 $F_τ$ are undistorted.

30 pages, 18 figures. Accepted for publication in Publ. Mat. on 1 September 2020

Countries

Australia, Spain

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
University of Melbourne
Australia
Universitat Politècnica de Catalunya
Spain
Royal Holloway University of London
United Kingdom
Autonomous University of Barcelona
Spain

Keywords

Generators, relations, and presentations of groups, Irrational-slope, irrational-slope, Distortion, Group Theory (math.GR), Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups, Normal forms, Grups finits, Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups, Grups infinits, :Matemàtiques i estadística::Àlgebra::Teoria de grups [Àrees temàtiques de la UPC], Thompson’s group, normal forms, FOS: Mathematics, :20 Group theory and generalizations::20F Special aspects of infinite or finite groups [Classificació AMS], distortion, Group theory, 20F65, Geometric group theory, Thompson's group, Mathematics - Group Theory

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