Geometric Group Theory (eBook)

Contents 6
Preface 7
Totally Disconnected, Locally Compact Groups as Geometric Objects 8
1. Introduction 8
2. Fat points the space of compact, open subgroups
3. Quasiflats flat subgroups and eigenfactors
4. Asymptotic information space of directions
5. Parabolics and contraction groups 25
References 26
Computational Explorations in Thompson’s Group F 28
1. Introduction 28
2. Background on Thompson’s group 29
and amenability 29
3. Algorithms and programs 31
4. Computational results concerning amenability 33
5. Computational results concerning the growth of 35
6. Rate of escape of random walks and dead-ends in 39
References 41
On the Surjunctivity of Artinian Linear Cellu-lar Automata over Residually Finite Groups 43
1. Introduction 43
2. Artinian modules 45
3. Proof of the main result 48
References 49
Some Residually Finite Groups Satisfying Laws 51
References 55
Classifying Spaces for Wallpaper Groups 57
Introduction 57
1. Background 59
2. Classifying spaces of wallpaper groups 61
References 68
A General Construction of JSJ Decompositions 71
1. Introduction 71
2. Assumptions and notations 72
3. Deformation spaces 73
4. The JSJ deformation space 75
5. The compatibility JSJ tree 77
References 79
D´ ecompositions de Groupes par Produit Direct et Groupes de Coxeter 80
1. Introduction 81
2. Premiers exemples 82
3. D ´ ecompositions de sous-groupes de groupes alg´ ebriques 90
4. Groupes de Coxeter et groupes d’Artin 94
5. Variation sur la notion d’ind ´ ecomposabilit´ e 98
6. Conditions Max et Min 98
7. Groupes ` a quotients major´ es 100
8. Majorations de nombres de facteurs directs 102
Abridged English version 103
References 105
Limit Groups of Equationally Noetherian Groups 108
1. Introduction 108
2. First properties 111
3. Factor sets 116
References 123
Solution of the Conjugacy Problem and Malnormality of Subgroups in Certain Relative Small Cancellation Group Presentations 125
Introduction 125
1. Preliminaries on maps 132
2. The layer structure of 136
3. Proofs of the main results 156
References 171
Solution of the Membership Problem for Magnus Subgroups in Certain One- Relator Free Products 173
Introduction 173
1. Preliminary results on words and diagrams 175
2. Piece configurations of 1-corner regions and 2- corner regions 186
3. Proof of the theorem 194
References 199
Conjugacy and Centralizers for Iwip Automorphisms of Free Groups 200
1. Introduction 200
2. Graphs, gates, turns, train tracks 202
3. Graph morphisms and train track maps 204
4. Invariant 208
trees 208
5. Iterating an automorphism 212
6. Eigensegments and their lifts 214
7. 216
Blowing 216
up vertices of a train track 216
8. The lifting theorem 221
9. The algorithm 224
References 226
Algebraic Extensions in Free Groups 228
1. Introduction 228
2. Preliminaries 230
3. Algebraic extensions 236
4. Abstract properties of subgroups 246
5. Some open questions 254
References 255