An irrational-slope Thompson’s group

• Burillo, Jos´e ^[3] ; Nucinkis, Brita ^[1] ; Reeves, Lawrence ^[2]
  1. [1] University of London

     University of London

     Reino Unido

     
  2. [2] University of Melbourne

     University of Melbourne

     Australia

     
  3. [3] Universitat Polit`ecnica de Catalunya. Departament de Matem`atiques

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• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 65, Nº 2, 2021, págs. 809-839
• Idioma: inglés
• DOI: 10.5565/publmat6522112
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• Resumen

  • The purpose of this paper is to study the properties of the irrational-slope Thompson’s group Fτ 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 Fτ are undistorted.

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