The Chameleon Groups Of Richard J Thompson Automorphisms And Dynamics

The Further Chameleon Groups of Richard Thompson and Graham Higman: Automorphisms via Dynamics for the Higman-Thompson Groups $G_{n,r}$

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The Chameleon Groups of Richard J. Thompson: Automorphisms and Dynamics

Robert Bieri and Ralph Strebel

Richard Thompson's famous group F has the striking property that it can be realized as a dense subgroup of the group of all orientation-preserving homeomorphisms of the unit interval, but it can also be given by a simple 2-generator-2-relator presentation, in fact as the fundamental group of an aspherical complex with only two cells in each dimension. This monograph studies a natural generalization of F that also includes Melanie Stein's generalized F-groups. The main aims of this monograph are the determination of isomorphisms among the generalized F -groups and the study of their automorphism groups. This book is aimed at graduate students (or teachers of graduate students) interested in a class of examples of torsion-free infinite groups with elements and composition that are easy to describe and work with, but have unusual properties and surprisingly small presentations in terms of generators and defining relations.