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An Introduction to Knot Theory : Graduate Texts in Mathematics - W.B.Raymond Lickorish

An Introduction to Knot Theory

Graduate Texts in Mathematics

Hardcover

Published: 3rd October 1997
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A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.

W.B.R. Lickorish An Introduction to Knot Theory "This essential introduction to vital areas of mathematics with connections to physics, while intended for graduate students, should fall within the ken of motivated upper-division undergraduates."--CHOICE

A beginning for Knot Theory
Seifert surfaces and knot factorization
The Jones polynomial
Geometry of alternating links
The Jones polynomial of an alternating link
The Alexander polynomial
Covering spaces
The Conway polynomial, signatures and slice knots
Cylic branched covers and the Goeritz matrix
The Arf invariant and the Jones polynomial
The fundamental group
Obtaining three-manifolds by surgery on S3
Three-manifold invariants from the Jones polynomial
Methods for calculating quantum invariants
Generalizations of the Jones polynomial
Exploring the HOMFLY and Kauffman polynomials
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387982540
ISBN-10: 038798254X
Series: Graduate Texts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 204
Published: 3rd October 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.6 x 16.4  x 1.8
Weight (kg): 0.5