**Contemporary Mathematics**

Volume: 394;
2006;
234 pp;
Softcover

MSC: Primary 20;
Secondary 55; 57

Print ISBN: 978-0-8218-3756-6

Product Code: CONM/394

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-7984-9
Product Code: CONM/394.E**

List Price: $75.00

Individual Member Price: $60.00

# Topological and Asymptotic Aspects of Group Theory

Share this page *Edited by *
*Rostislav Grigorchuk; Michael Mihalik; Mark Sapir; Zoran Šuniḱ*

The articles in this volume are based on the talks given at two special sessions at the AMS Sectional meetings held in 2004. The articles cover various topological and asymptotic aspects of group theory such as hyperbolic and relatively hyperbolic groups, asymptotic cones, Thompson's group, Nielsen fixed point theory, homology, groups acting on trees, groups generated by finite automata, iterated monodromy groups, random walks on finitely generated groups, heat kernels, and currents on free groups.

#### Table of Contents

# Table of Contents

## Topological and Asymptotic Aspects of Group Theory

- Contents vii8 free
- Preface ix10 free
- A dichotomy for finitely generated subgroups of word hyperbolic groups 112 free
- Some solvable automaton groups 1122
- Quotient tests and random walks in computational group theory 3142
- 1. Decision problems and quotient tests 3142
- 2. Quotient test for the identity problem: non-amenable quotient group 3445
- 3. Quotient test for the identity problem: amenable quotient groups 3546
- 4. The role of the mixing time 3647
- 5. Quotient tests for the word problem 4051
- 6. Quotient tests for the conjugacy problem 4354
- References 4455

- The homology of Richard Thompson's group F 4758
- On the growth of iterated monodromy groups 6172
- On Bestvina-Mess formula 7788
- Symmetric random walks on certain amalgamated free product groups 8798
- Homology of tree braid groups 101112
- Associativity and Thompson's group 113124
- Traveller Salesman Property and Richard Thompson's group F 137148
- On groups with periodic products of commutators 143154
- Currents on free groups 149160
- Heat kernels, theta identities, and zeta functions on cyclic groups 177188
- The Nielsen fixed point structure for homotopy idempotents on surfaces 191202
- Thompson's group F is not Kähler 197208
- Groups with non-simply connected asymptotic cones 203214
- Relative Dehn functions of amalgamated products and HNN-extensions 209220
- Endomorphisms of the finitary group of isometries of the binary tree 221232

#### Readership

Graduate students and research mathematicians interested in geometric group theory.