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.
- | Author: Patrick Dehornoy
- | Publisher: Cambridge University Press
- | Publication Date: 9-Sep-21
- | Number of Pages: 258 pages
- | Language: English
- | Binding: Paperback
- | ISBN-10: 1108925863
- | ISBN-13: 9781108925860
