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Knots and Links - Peter R. Cromwell

Paperback

Published: 18th January 2005
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Knots and links are studied by mathematicians, and are also finding increasing application in chemistry and biology. Many naturally occurring questions are often simple to state, yet finding the answers may require ideas from the forefront of research. This readable and richly illustrated book explores selected topics in depth in a way that makes contemporary mathematics accessible to an undergraduate audience. It can be used for upper-division courses, and assumes only knowledge of basic algebra and elementary topology. Together with standard topics, the book explains: polygonal and smooth presentations; the surgery equivalence of surfaces; the behaviour of invariants under factorisation and the satellite construction; the arithmetic of Conway's rational tangles; arc presentations. Alongside the systematic development of the main theory, there are discussion sections that cover historical aspects, motivation, possible extensions, and applications. Many examples and exercises are included to show both the power and limitations of the techniques developed.

"The book has a satisfying, unifying goalclear prose, systematic rigor, attractive layout, and copious diagrams all add to the overall appeal. Highly recommended." Choice "The book under review wil be of great help to anyone who sudies or teaches knot theory. It reflects adequately the contemporary state of the parts of the theory it covers, and the reader finishes it with a natural feeling that at some time in the future, knot theory will become an obligatory study for each math undergraduate..." Mathematical Reviews, Sergei K. Lando

Preface
Introduction
A topologistÆs toolkit
Link diagrams
Constructions and decompositions of links
Spanning surfaces and genus
Matrix invariants
The Alexander-Conway polynomial
Rational tangles
More polynomials
Closed braids and arc presentations
Knot diagrams
Numerical invariants
Properties
Polynomials
Polygon coordinates
Family properties
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521548311
ISBN-10: 0521548314
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 348
Published: 18th January 2005
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.7 x 17.4  x 1.8
Weight (kg): 0.57