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An Introduction to Knot Theory : Introduction to Knot Theory - W.B.Raymond Lickorish

An Introduction to Knot Theory

Introduction to Knot Theory

Hardcover Published: 3rd October 1997
ISBN: 9780387982540
Number Of Pages: 204

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This volume is an introduction to mathematical knot theory - the theory of knots and links of simple closed curves in three-dimensional space. It consists of a selection of topics that graduate students have found to be a successful introduction to the field. Three distinct techniques are employed: geometric topology manoeuvres; combinatorics; and algebraic topology. Each topic is developed until significant results are achieved, and chapters end with exercises and brief accounts of state-of-the-art research. What may reasonably be referred to as knot theory has expanded enormously over the last decade, and while the author describes important discoveries from 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 understandable style. Thus, this constitutes a comprehensive introduction to the field, presenting modern developments in the context of classical material. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are plentiful and well done. Written by an internationally known expert in the field, this volume will appeal to graduate students, mathematicians, and physicists with a mathematical background who wish to gain new insights in this area.

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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: Introduction to Knot Theory
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 204
Published: 3rd October 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.21 x 16.2  x 1.52
Weight (kg): 0.44

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