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25 Remote Warehouse Mathematics- Abstract Algebra

Graduate Texts in Mathematics #175: An Introduction to Knot Theory

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Graduate Texts in Mathematics #175: An Introduction to Knot Theory Cover

 

Synopses & Reviews

Publisher Comments:

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.

Table of Contents

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.

Product Details

ISBN:
9781461268697
Author:
Lickorish, W. B. Raymond
Publisher:
Springer
Subject:
Mathematics-Abstract Algebra
Subject:
Topology
Subject:
Manifolds and Cell Complexes (incl. Diff.Topology)
Subject:
Group Theory and Generalizations
Subject:
Theoretical, Mathematical and Computational Physics
Edition Description:
Softcover reprint of the original 1st ed. 1997
Series:
Graduate Texts in Mathematics
Series Volume:
175
Publication Date:
20121031
Binding:
TRADE PAPER
Language:
English
Pages:
214
Dimensions:
235 x 155 mm

Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Topology
Science and Mathematics » Physics » Astrophysics
Science and Mathematics » Physics » General
Science and Mathematics » Physics » Math

Graduate Texts in Mathematics #175: An Introduction to Knot Theory New Trade Paper
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