The calculus of braids : an introduction, and beyond

著者

書誌事項

The calculus of braids : an introduction, and beyond

Patrick Dehornoy ; translated by Danièle Gibbons, Greg Gibbons

(London Mathematical Society student texts, 100)

Cambridge University Press, 2021

  • : hardback
タイトル別名

Calcul des tresses

統一タイトル

Calcul des tresses

大学図書館所蔵 件 / 全10件

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注記

"Originally published in French as Le calcul des tresses by Calvage et Mounet, 2019"--T.p. verso

Includes bibliographical references (p. 242-243) and index

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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詳細情報

  • NII書誌ID(NCID)
    BC1038215X
  • ISBN
    • 9781108843942
  • LCCN
    2021029783
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    fre
  • 出版地
    Cambridge
  • ページ数/冊数
    xii, 245 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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