Cover Image
Read Now

Classical Topology and Combinatorial Group Theory

In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topolo...

Full description

Bibliographic Details
Main Author: Stillwell, John
Format: eBook
Language:English
Published: New York, NY Springer New York 1980, 1980
Edition:1st ed. 1980
Series:Graduate Texts in Mathematics
Subjects:
Group Theory And Generalizations
Group Theory
Topology
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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 Poincaré’s Method for Computing Presentations’
  • 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 Dehn’s 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 Schreier’s 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

Similar Items