Topological and Asymptotic Aspects of Group Theory

Preface ix

A dichotomy for finitely generated subgroups of word hyperbolic groups

Goulnara N. Arzhantseva 1

Some solvable automaton groups

Laurent Bartholdi and Zoran ˇSuni´k 11

Quotient tests and random walks in computational group theory

Alexandre V. Borovik and Alexei G. Myasnikov 31

The homology of Richard Thompson’s group F

Kenneth S. Brown 47

On the growth of iterated monodromy groups

Kai-Uwe Bux and Rodrigo P´erez 61

On Bestvina-Mess formula

Alexander N. Dranishnikov 77

Symmetric random walks on certain amalgamated free product groups

Ken Dykema 87

Homology of tree braid groups

Daniel Farley 101

Associativity and Thompson’s group

Ross Geoghegan and Fernando Guzm´an 113

Traveller Salesman Property and Richard Thompson’s group F

Victor S. Guba 137

On groups with periodic products of commutators

Sergei V. Ivanov 143

Currents on free groups

Ilya Kapovich 149

Heat kernels, theta identities, and zeta functions on cyclic groups

Anders Karlsson and Markus Neuhauser 177

The Nielsen fixed point structure for homotopy idempotents on surfaces

Michael R. Kelly 191

Thompson’s group F is not K¨ahler

Terrence Napier and Mohan Ramachandran 197

vii

viii CONTENTS

Groups with non-simply connected asymptotic cones

Alexander Yu. Ol’shanskii and Mark V. Sapir 203

Relative Dehn functions of amalgamated products and HNN-extensions

Denis V. Osin 209

Endomorphisms of the finitary group of isometries of the binary tree

Andrew M. Brunner and Said N. Sidki 221