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Introduction to Knot Theory

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Introduction to Knot Theory Cover

 

Synopses & Reviews

Publisher Comments:

Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, its accessible treatment requires no previous knowledge of algebraic topology.

Starting with basic definitions of knots and knot types, the text proceeds to examinations of fundamental and free groups. A survey of the historic foundation for the notion of group presentation is followed by a careful proof of the theorem of Tietze and several examples of its use. Subsequent chapters explore the calculation of fundamental groups, the presentation of a knot group, the free calculus and the elementary ideals, and the knot polynomials and their characteristic properties. The text concludes with three helpful appendixes and a guide to the literature.

Synopsis:

Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature." 1963 edition.

Synopsis:

Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature." 1963 edition.

Table of Contents

Prerequisites
Chapter 1. Knots and Knot Types
Chapter 2. The Fundamental Group
Chapter 3. The Free Groups
Chapter 4. Presentation of Groups
Chapter 5. Calculation of Fundamental Groups
Chapter 6. Presentation of a Knot Group
Chapter 7. The Free Calculus and the Elementary Ideals
Chapter 8. The Knot Polynomials
Chapter 9. Characteristic Properties of the Knot Polynomials
Appendix I. Differentiable Knots are Tame
Appendix II. Categories and groupoids
Appendix III. Proof of the van Kampen theorem
Guide to the Literature
Bibliography
Index

Product Details

ISBN:
9780486468945
Author:
Crowell, Richard H
Publisher:
Dover Publications
Author:
Fox, Ralph H.
Author:
Crowell, Richard H.
Author:
Mathematics
Subject:
Topology
Subject:
Topology - General
Subject:
Knot theory
Subject:
MATHEMATICS / Topology
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20080931
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
192
Dimensions:
9.25 x 6.13 in 0.54 lb

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Science and Mathematics » Mathematics » Topology

Introduction to Knot Theory New Trade Paper
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Product details 192 pages Dover Publications - English 9780486468945 Reviews:
"Synopsis" by ,
Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature." 1963 edition.
"Synopsis" by ,
Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature." 1963 edition.
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