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Combinatorial and Geometric Group Theory pp 279–296Cite as

Some Graphs Related to Thompson’s Group F

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Abstract

The Schreier graphs of Thompson’s group F with respect to the stabilizer of 1/2 and generators x 0 and x 1 , and of its unitary representation in L 2 ([0, 1]) induced by the standard action on the interval [0, 1] are explicitly described. The coamenability of the stabilizers of any finite set of dyadic rational numbers is established. The induced subgraph of the right Cayley graph of the positive monoid of F containing all the vertices of the form x n v, where n ≥ 0 and v is any word over the alphabet {x 0 , x 1 }, is constructed. It is proved that the latter graph is non-amenable.

The author was supported by NSF grants DMS-0600975 and DMS-0456185.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Dmytro Savchuk

Authors
  1. Dmytro Savchuk
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Editor information

Editors and Affiliations

  1. Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany

    Oleg Bogopolski

  2. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada

    Inna Bumagin

  3. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St., West, Montreal, Quebec, H3A 2K6, Canada

    Olga Kharlampovich

  4. Departament de Matematica Aplicada III, EPSEM — Universitat Politècnica de Catalunya, Av. Bases de Manresa 61-73, 08242, Manresa, Barcelona, Spain

    Enric Ventura

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Savchuk, D. (2010). Some Graphs Related to Thompson’s Group F . In: Bogopolski, O., Bumagin, I., Kharlampovich, O., Ventura, E. (eds) Combinatorial and Geometric Group Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9911-5_12

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