Some Graphs Related to Thompson’s Group F

  • Dmytro Savchuk
Part of the Trends in Mathematics book series (TM)


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.

Mathematics Subject Classification (2000)



Thompson’s group amenability Schreier graphs Cayley graphs 


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© Springer Basel AG 2010

Authors and Affiliations

  • Dmytro Savchuk
    • 1
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

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