Automorphisms of Surfaces After Nielsen and ThurstonThis book, which grew out of Steven Bleiler's lecture notes from a course given by Andrew Casson at the University of Texas, is designed to serve as an introduction to the applications of hyperbolic geometry to low dimensional topology. In particular it provides a concise exposition of the work of Neilsen and Thurston on the automorphisms of surfaces. The reader requires only an understanding of basic topology and linear algebra, while the early chapters on hyperbolic geometry and geometric structures on surfaces can profitably be read by anyone with a knowledge of standard Euclidean geometry desiring to learn more abour other 'geometric structures'. |
Contents
Preface | 11 |
0 Introduction | 1 |
1 The Hyperbolic Plane H² | 3 |
2 Hyperbolic structures on surfaces | 17 |
3 Geodesic laminations | 38 |
4 Structure of geodesic laminations | 60 |
5 Surface automorphisms | 75 |
6 PseudoAnosov automorphisms | 89 |
References | 103 |
Index | |
Other editions - View all
Automorphisms of Surfaces after Nielsen and Thurston Andrew J. Casson,Steven A. Bleiler No preview available - 1988 |
Automorphisms of Surfaces After Nielsen and Thurston Andrew J Casson,Steven A Bleiler No preview available - 2014 |
Common terms and phrases
Aut(F automorphism axis boundary components boundary leaf C₁ C₂ chart circle at infinity closed geodesic closed hyperbolic surface closed leaves closed orientable hyperbolic closure compact complete hyperbolic surface contained contracting fixed points converges defined Definition Dehn twist dense disjoint union endpoints essential 1-submanifold Euclidean F₁ F₂ Figure finite area finite sided polygon fixed points follows geodesic boundary geodesic lamination h₁ half-plane model Hausdorff distance hence homeomorphism homotopic Hopf-Rinow Theorem hyperbolic distance hyperbolic structure implies integer invariant inversion isometry isotopic K₁ Lemma lift of hm line field matrix metric minimal intersection neighborhood non-empty non-periodic irreducible automorphism orientable hyperbolic surface orientation-preserving parabolic Poincare disk preimage principal region Proof pseudo-Anosov PT(F rectangle Remark separatrix sequence shows simple closed geodesic stable interval surface automorphisms surface F tangent Theorem transverse measure union of geodesics union of simple unique universal cover UT(F vertices