Algorithmic and Computer Methods for Three-Manifolds

ISBN-13: 9789048149254 / Angielski / Miękka / 2010 / 337 str.

A.T. Fomenko;S.V. Matveev

Opis

This monograph presents a comprehensive coverage of three-dimensional topology, as well as exploring some of its frontiers. Many important applied problems of mechanics and theoretical physics can be reduced to algorithmic problems of three-dimensional topology, which can then be solved using computers. Although much progress in this field has been made in recent years, these results have not been readily accessible to a wider audience up to now. This book is based on courses the authors have given over several years, and summarises the most outstanding achievements of modern computer topology. Audience: This book will be of interest to graduate students and researchers whose work involves such diverse disciplines as physics, mathematics, computer programmes for spline theory and its applications, geometrical modelling, geometry, and topology. The illustrations by A.T. Fomenko, drawn especially for this work, add great value and extra appeal.

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.