Algorithmic and Computer Methods for Three-Manifolds

ISBN-13: 9780792347705 / Angielski / Twarda / 1997 / 337 str.

A. T. Fomenko; S. V. Matveev

Opis

One service mathematics has rendered the human race. It has put common sense back where it belongs. It has put common sense back where it belongs, on the topmost shelf next to the dusty canister labelled discarded nonsense. Eric TBell Every picture tells a story. Advenisement for for Sloan's backache and kidney oils, 1907 The book you have in your hands as you are reading this, is a text on3-dimensional topology. It can serve as a pretty comprehensive text book on the subject. On the other hand, it frequently gets to the frontiers of current research in the topic. If pressed, I would initially classify it as a monograph, but, thanks to the over three hundred illustrations of the geometrical ideas involved, as a rather accessible one, and hence suitable for advanced classes. The style is somewhat informal; more or less like orally presented lectures, and the illustrations more than make up for all the visual aids and handwaving one has at one's command during an actual presentation.

Recenzje

`I really enjoyed this book; it is great fun and full of enthusiasm for the subject. ... Furthermore, there are some excellent figures, which bring the book to life and often show really clearly what is going on.'
Bulletin of the London Mathematical Society, 32 (2000)
`This book is an attractive and comprehensive introduction to three-dimensional topology. The book is readable and inviting. Its many illustrations make it particularly accessible. This book promises to be a valuable text and reference for an exciting area of mathematics.'
SIAM Review, 41:2 (1999)

Spis treści

1. Preliminary Information. 2. Surfaces. 3. The Homeotopy Group of a Surface. 4. The Presentation of Three-Dimensional Manifolds by the Identification of Faces of Polyhedra. 5. Heegaard Splittings and Heegaard Diagrams. 6. Algorithmic Recognition of the Sphere. 7. Connected Sums. 8. Knots and Links. 9. Surgery Along Links. 10. Seifert Manifolds. 11. Class H. 12. The Haken Method. Comments on the Figures. References. Index.