Knots and Links

A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.

Peter R. Cromwell (Author)

9780521548311, Cambridge University Press

Paperback, published 14 October 2004

348 pages, 236 b/w illus. 9 tables 118 exercises
24.4 x 17 x 1.8 cm, 0.57 kg

"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

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 2004 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.

Preface
1. Introduction
2. A topologist's toolkit
3. Link diagrams
4. Constructions and decompositions of links
5. Spanning surfaces and genus
6. Matrix invariants
7. The Alexander-Conway polynomial
8. Rational tangles
9. More polynomials
10. Closed braids and arc presentations
Appendix A. Knot diagrams
Appendix B. Numerical invariants
Appendix C. Properties
Appendix D. Polynomials
Appendix E. Polygon coordinates
Appendix F. Family properties
Bibliography
Index.

Subject Areas: Topology [PBP], Geometry [PBM]