Knots and Links

ISBN-13: 9780521548311 / Angielski / Miękka / 2004 / 348 str.

Peter R. Cromwell

Opis

Knot theory is the study of embeddings of circles in space. Peter Cromwell has written a textbook on knot theory designed for use in advanced undergraduate or beginning graduate-level courses. The exposition is detailed and careful yet engaging and full of motivation. Numerous examples and exercises serve to help students through the material, while an instructor's manual is available online.

Recenzje

"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

Spis treści

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.