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Classical topology and combinatorial group theory

Author: John Stillwell
Publisher: New York : Springer-Verlag, 1995.
Series: Graduate texts in mathematics, 72.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:

This introduction to topology stresses geometric aspects, focusing on historical background and visual interpretation of results. The 2nd edition offers 300 illustrations, numerous exercises,  Read more...

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Document Type: Book
All Authors / Contributors: John Stillwell
ISBN: 0387979700 9780387979700 3540979700 9783540979708
OCLC Number: 33243715
Notes: "Corrected second printing"--Title page verso.
Description: xii, 334 pages : illustrations ; 25 cm.
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 Poincare'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.- 8.5 Branched Coverings.- 9 Unsolvable Problems.- 9.1 Computation.- 9.2 HNN Extensions.- 9.3 Unsolvable Problems in Group Theory.- 9.4 The Homeomorphism Problem.- Bibliography and Chronology.
Series Title: Graduate texts in mathematics, 72.
Responsibility: John Stillwell ; illustrated with 312 figures by the author.

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