Commensurations and Subgroups of Finite Index of Thompson's Group F

José Burillo, Sean Cleary and Claas Röver

Abstract

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

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