Some graphs related to Thompson's group F
Abstract
The Schreier graphs of Thompson's group F with respect to the stabilizer of 1/2 and generators x0 and x1, and of its unitary representation in L2([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 xnv, where n>=0 and v is any word over the alphabet x0, x1, is constructed. It is proved that the latter graph is non-amenable.
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