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The Calculus of Braids: London Mathematical Society Student Texts, cartea 100

Autor Patrick Dehornoy
en Limba Engleză Paperback – 8 sep 2021
Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results concerning them. This book demonstrates that there is a resoundingly positive response to this question: braids are fascinating objects, with a variety of rich mathematical properties and potential applications. A special emphasis is placed on the algorithmic aspects and on what can be called the 'calculus of braids', in particular the problem of isotopy. Prerequisites are kept to a minimum, with most results being established from scratch. An appendix at the end of each chapter gives a detailed introduction to the more advanced notions required, including monoids and group presentations. Also included is a range of carefully selected exercises to help the reader test their knowledge, with solutions available.
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Specificații

ISBN-13: 9781108925860
ISBN-10: 1108925863
Pagini: 220
Dimensiuni: 150 x 230 x 16 mm
Greutate: 0.38 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria London Mathematical Society Student Texts

Locul publicării:Cambridge, United Kingdom

Cuprins

1. Geometric braids; 2. Braid groups; 3. Braid monoids; 4. The greedy normal form; 5. The Artin representation; 6. Handle reduction; 7. The Dynnikov coordinates; 8. A few avenues of investigation; 9. Solutions to the exercises; Glossary; References; Index.

Notă biografică


Descriere

This introduction to braid groups keeps prerequisites to a minimum, while discussing their rich mathematical properties and applications.