DEHN’S ALGORITHM REVISITED, WITH APPLICATIONS TO SIMPLE CURVES ON SURFACES

Chapters in this book

1. Frontmatter i
2. CONTENTS v
3. PREFACE vii
4. I. Combinatorial Group Theory
5. PROBLEMS IN COMBINATORIAL GROUP THEORY 3
6. POINCARÉ DUALITY GROUPS OF DIMENSION TWO ARE SURFACE GROUPS 35
7. HOW TO GENERALIZE ONE-RELATOR GROUP THEORY 53
8. GRAPHICAL THEORY OF AUTOMORPHISMS OF FREE GROUPS 79
9. PEAK REDUCTION AND AUTOMORPHISMS OF FREE GROUPS AND FREE PRODUCTS 107
10. NONSINGULAR EQUATIONS OF SMALL WEIGHT OVER GROUPS 121
11. GRAPH-THEORETIC LEMMA AND GROUP-EMBEDDINGS 145
12. THE TODD-COXETER PROCESS, USING GRAPHS 157
13. A SUBGROUP THEOREM FOR PREGROUPS 163
14. GROUPS WITH A RATIONAL CROSS-SECTION 175
15. ON THE RATIONAL GROWTH OF VIRTUALLY NILPOTENT GROUPS 185
16. SJOGREN’S THEOREM FOR DIMENSION SUBGROUPS - THE METABELIAN CASE 197
17. ON GROUP PRESENTATIONS, COPRODUCTS AND INVERSES 213
18. ON COMPLEXES DOMINATED BY A TWO-COMPLEX 221
19. SUBCOMPLEXES OF TWO-COMPLEXES AND PROJECTIVE CROSSED MODULES 255
20. LENGTH FUNCTIONS OF GROUP ACTIONS ON A-TREES 265
21. II. Very Low Dimensional Topology
22. RESIDUAL FINITENESS FOR 3-MANIFOLDS 379
23. THE NIELSEN-THURSTON THEORY OF SURFACE AUTOMORPHISMS 397
24. WHITEHEAD GROUPS OF CERTAIN HYPERBOLIC MANIFOLDS, II 415
25. CHARACTERIZATION OF FINITE SUBGROUPS OF THE MAPPING-CLASS GROUP 433
26. A SEQUENCE OF PSEUDO-ANOSOV DIFFEOMORPHISMS 443
27. DEHN’S ALGORITHM REVISITED, WITH APPLICATIONS TO SIMPLE CURVES ON SURFACES 451
28. PATHS OF GEODESICS AND GEOMETRIC INTERSECTION NUMBERS: I 479
29. PATHS OF GEODESICS AND GEOMETRIC INTERSECTION NUMBERS: II 501
30. SELECTED PROBLEMS 545
31. Backmatter 552