Two-dimensional homotopy and combinatorial group theory

Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents\0......Page 6
Editors\' Preface\0......Page 10
Addresses of Authors\0......Page 12
1 Complexes of Low Dimensions and Group Presentations\0......Page 14
2 Simple-Homotopy and Low Dimensions\0......Page 24
3 P.L. Embeddings of 2-Complexes into Manifolds\0......Page 42
4 Three Conjectures and Further Problems\0......Page 57
1 Techniques in Homotopy\0......Page 64
2 Homotopy Groups for 2-Complexes\0......Page 75
3 Equivariant World for 2-Complexes\0......Page 88
4 Mac Lane-Whitehead Algebraic Types\0......Page 101
1 Bias Invariant & Homology Classification\0......Page 110
2 Classifications for Finite Abelian irl..\0......Page 124
3 Classifications for Non-Finite 7r1 (with Cynthia Hog-Angeloni)\0......Page 130
1 Introduction\0......Page 138
2 Crossed and Precrossed Modules\0......Page 139
3 On the Second Homotopy Module of a 2-Complex\0......Page 153
4 Identity Properties\0......Page 161
1 The Theory of Pictures\0......Page 170
2 Generation of H2\0......Page 180
3 Applications and Results\0......Page 189
1 Introduction\0......Page 202
2 Decidability and Dehn\'s Algorithm\0......Page 203
3 Cayley Graph and van Kampen Diagrams\0......Page 205
4 Word Hyperbolic Groups and Combings\0......Page 210
5 Curvature Tests\0......Page 216
VII Fox Ideals, A(-Torsion and Applications to Groups and 3-Manifolds\0......Page 232
1 Fox ideals\0......Page 233
7 Topological Embeddings of 2-Spheres into 1-Connected\0......Page 0
and the homological dimension of a group\0......Page 238
3 JI-torsion: Basic theory\0......Page 243
4 JV1(G), Nielsen equivalence of generating systems and Heegaard splittings\0......Page 246
5 N-torsion as generalization of the bias and (simple)-homotopy of (G, m)-complexes\0......Page 258
1 3-Manifolds\0......Page 264
2 Singular 3-Manifolds\0......Page 287
1 A Cancellation Theorem for 2-Complexes\0......Page 294
2 Stable Classification of 4-Manifolds\0......Page 299
3 A Cancellation Theorem for Topological 4-Manifolds\0......Page 303
4-Manifolds\0......Page 309
5 A Non-Cancellation Example for Simple-Homotopy Equivalent Topological 4-Manifolds\0......Page 312
6 Application of Cancellation to Exotic Structures on 4-Manifolds\0......Page 315
4-Manifolds and Pseudo-free Group Actions\0......Page 318
1 Introduction\0......Page 322
2 The Context of Whitehead\'s Question\0......Page 323
3 Structural Results\0......Page 325
4 Reductions, Evidence and Test Cases\0......Page 327
5 On the 7rl-Kernel\0......Page 333
6 Acyclic Coverings\0......Page 335
7 Finitely Generated Perfect Subgroups\0......Page 339
8 Kaplansky\'s Theorem\0......Page 341
9 Framed Links\0......Page 343
10 Open Questions (with J. Howie)\0......Page 346
1 Introduction\0......Page 348
2 Collapsing\0......Page 351
3 Some Special Ways of Collapsing P2 x I\0......Page 352
4 1-Collapsibility Modulo 2-Expansions\0......Page 361
5 Zeeman Conjecture for Special Polyhedra\0......Page 362
6 Generalizing (Z) to Higher Dimensions\0......Page 374
7 Open Problems\0......Page 376
1 Introduction\0......Page 378
2 Strategies and Characterizations\0......Page 379
3 Q**-Transformations and Presentations of Free Products\0......Page 386
4 Some Further Results\0......Page 393
Bibliography\0......Page 394
Index\0......Page 421