The calculus of braids
著者
書誌事項
The calculus of braids
（London Mathematical Society student texts, 100）
Cambridge University Press, 2021
- hbk.
- タイトル別名
-
The calculus of braids : an introduction, and beyond
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内容説明・目次
内容説明
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.
目次
- 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.
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