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9780471355441

Topology of Surfaces, Knots, and Manifolds

by
  • ISBN13:

    9780471355441

  • ISBN10:

    0471355445

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2001-01-10
  • Publisher: Wiley

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Summary

Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links--the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry." The result is a book that provides solid coverage of the mathematics underlying these topics.

Author Biography

Stephan C. Carlson is the author of Topology of Surfaces, Knots, and Manifolds, published by Wiley.

Table of Contents

Introduction and Intuitive Ideas
1(25)
What Is Topology?
1(6)
Getting More Formal
7(4)
Functions and Homeomorphisms
11(7)
Constructing Objects from Plane Models
18(4)
Chapter Summary
22(1)
Supplementary Exercises
22(3)
Manifolds
25(20)
Basic Definitions and Curves
25(7)
Surfaces
32(2)
Compact Surfaces and Plane Models
34(6)
Three-dimensional Manifolds
40(3)
Chapter Summary
43(1)
Supplementary Exercises
44(1)
Classification of Compact Surfaces
45(23)
Connected Sums: New Surfaces from Old
45(3)
The Algebra of Surfaces
48(12)
The Classification Theorem: Preliminary Ideas
60(3)
The Proof of the Classification Theorem
63(3)
Chapter Summary
66(1)
Supplementary Exercises
67(1)
Putting More Structure on the Surfaces
68(31)
Tilings on Surfaces and the Euler Characteristic
68(11)
Patterns, Complexes, and Regularity
79(11)
Coloring Maps on Surfaces
90(7)
Chapter Summary
97(1)
Supplementary Exercises
97(2)
Graphs and Topology
99(1)
What is a Graph?
99(22)
Paths in Graphs
104(6)
Embedding Graphs in Surfaces
110(8)
Chapter Summary
118(1)
Supplementary Exercises
119(2)
Knot Theory
121(30)
Knots and Links: the Basics
122(7)
Oriented Links and Linking Number
129(4)
Tricolorability of Knots and Links
133(4)
Polynomial Invariants of Knots and Links
137(10)
Chapter Summary
147(1)
Supplementary Exercises
148(3)
Appendix 151(1)
References and Suggestions for Further Study 151(4)
Index 155

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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