Author | Stillwell, John. author |
---|---|
Title | Classical Topology and Combinatorial Group Theory [electronic resource] / by John Stillwell |
Imprint | New York, NY : Springer US, 1980 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0110-3 |
Descript | online resource |
0 Introduction and Foundations -- 0.1 The Fundamental Concepts and Problems of Topology -- 0.2 Simplicial Complexes -- 0.3 The Jordan Curve Theorem -- 0.4 Algorithms -- 0.5 Combinatorial Group Theory -- 1 Complex Analysis and Surface Topology -- 1.1 Riemann Surfaces -- 1.2 Nonorientable Surfaces -- 1.3 The Classification Theorem for Surfaces -- 1.4 Covering Surfaces -- 2 Graphs and Free Groups -- 2.1 Realization of Free Groups by Graphs -- 2.2 Realization of Subgroups -- 3 Foundations for the Fundamental Group -- 3.1 The Fundamental Group -- 3.2 The Fundamental Group of the Circle -- 3.3 Deformation Retracts -- 3.4 The Seifert-Van Kampen Theorem -- 3.5 Direct Products -- 4 Fundamental Groups of Complexes -- 4.1 Poincarรฉโs Method for Computing Presentationsโ -- 4.2 Examples -- 4.3 Surface Complexes and Subgroup Theorems -- 5 Homology Theory and Abelianization -- 5.1 Homology Theory -- 5.2 The Structure Theorem for Finitely Generated Abelian Groups -- 5.3 Abelianization -- 6 Curves on Surfaces -- 6.1 Dehnโs Algorithm -- 6.2 Simple Curves on Surfaces -- 6.3 Simplification of Simple Curves by Homeomorphisms -- 6.4 The Mapping Class Group of the Torus -- 7 Knots and Braids -- 7.1 Dehn and Schreierโs Analysis of the Torus Knot Groups -- 7.2 Cyclic Coverings -- 7.3 Braids -- 8 Three-Dimensional Manifolds -- 8.1 Open Problems in Three-Dimensional Topology -- 8.2 Polyhedral Schemata -- 8.3 Heegaard Splittings -- 8.4 Surgery 263 8.5 Branched Coverings -- Bibliography and Chronology