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Topology of Surfaces, Knots, and Manifolds

ISBN-10: 0471355445

ISBN-13: 9780471355441

Edition: 2001

Authors: Stephan C. Carlson

List price: $151.95
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Description:

Ideas and problems involving curves, surfaces and knots are presented here to introduce some basic ideas and problems concerning manifolds, especially one- and two-dimensional manifolds, via an intuition-based and example-driven approach.
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Book details

List price: $151.95
Copyright year: 2001
Publisher: John Wiley & Sons, Incorporated
Publication date: 1/1/2001
Binding: Hardcover
Pages: 176
Size: 6.25" wide x 9.25" long x 0.50" tall
Weight: 0.880
Language: English

Introduction and Intuitive Ideas
What Is Topology?
Getting More Formal
Functions and Homeomorphisms
Constructing Objects from Plane Models
Chapter Summary
Supplementary Exercises
Manifolds
Basic Definitions and Curves
Surfaces
Compact Surfaces and Plane Models
Three-dimensional Manifolds
Chapter Summary
Supplementary Exercises
Classification of Compact Surfaces
Connected Sums: New Surfaces from Old
The Algebra of Surfaces
The Classification Theorem: Preliminary Ideas
The Proof of the Classification Theorem
Chapter Summary
Supplementary Exercises
Putting More Structure on the Surfaces
Tilings on Surfaces and the Euler Characteristic
Patterns, Complexes, and Regularity
Coloring Maps on Surfaces
Chapter Summary
Supplementary Exercises
Graphs and Topology
What is a Graph?
Paths in Graphs
Embedding Graphs in Surfaces
Chapter Summary
Supplementary Exercises
Knot Theory
Knots and Links: the Basics
Oriented Links and Linking Number
Tricolorability of Knots and Links
Polynomial Invariants of Knots and Links
Chapter Summary
Supplementary Exercises
Appendix
References and Suggestions for Further Study
Index