Knots and Surfaces

by Gilbert, N. D.; Porter, T.

• ISBN13: 9780198533979
• ISBN10: 0198533977
• Format: Hardcover
• Copyright: 1995-01-26
• Publisher: Oxford University Press

Summary

This highly readable text details the interaction between the mathematical theory of knots and the theories of surfaces and group presentations. It expertly introduces several topics critical to the development of pure mathematics while providing an account of math "in action" in an unusual context. Beginning with a simple diagrammatic approach to the study of knots that reflects the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent research advances. Topics include topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations. The authors skillfully combine these topics to form a coherent and highly developed theory to explore and explain the accessible and intuitive problems of knots and surfaces to students and researchers in mathematics.

Table of Contents

Knots, Links, and Diagrams

Knot and Link Polynomials

Topological Spaces

Surfaces

The Arithmetic of Knots

Presentations of Groups

Graphs and Trees

Alexanders Matrices and Alexander Polynomials

The Fundamental Group

Van Kampen's Theorem

Applications of Van Kampen Theorem

Covering Spaces

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