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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Commensurations and subgroups of finite index of Thompson's group $F$

José Burillo, Sean Cleary and Claas E Röver

Geometry & Topology 12 (2008) 1701–1709
Abstract

We determine the abstract commensurator Com(F) of Thompson’s group F and describe it in terms of piecewise linear homeomorphisms of the real line. We show Com(F) is not finitely generated and determine which subgroups of finite index in F are isomorphic to F. We also show that the natural map from the commensurator group to the quasi-isometry group of F is injective.

Keywords
Thompson group, commensurator
Mathematical Subject Classification 2000
Primary: 20E34, 20F65
Secondary: 26A30, 20F28
References
Publication
Received: 9 November 2007
Revised: 9 May 2008
Accepted: 26 March 2008
Published: 19 June 2008
Proposed: Walter Neumann
Seconded: Benson Farb, Martin Bridson
Authors
José Burillo
Departament de Matemàtica Aplicada IV
Universitat Politècnica de Catalunya
Escola Politècnica Superior de Castelldefels
Avda. Del Canal Olímpic 15
08860 Castelldefels (Barcelona)
Spain
http://www-ma4.upc.edu/~burillo/
Sean Cleary
Department of Mathematics R8133
The City College of New York
Convent Ave & 138th
New York, NY 10031
USA
http://www.sci.ccny.cuny.edu/~cleary/
Claas E Röver
Department of Mathematics
University of Ireland, Galway
University Road
Galway
Ireland
http://www.maths.nuigalway.ie/~chew/