The calculus of braids : an introduction, and beyond

Author(s)

Bibliographic Information

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

Other Title

Calcul des tresses

Uniform Title

Calcul des tresses

Available at  / 10 libraries

Search this Book/Journal

Note

"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

Description and Table of Contents

Description

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.

Table of Contents

  • 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.

by "Nielsen BookData"

Related Books: 1-1 of 1

Details

  • NCID
    BC1038215X
  • ISBN
    • 9781108843942
  • LCCN
    2021029783
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Original Language Code
    fre
  • Place of Publication
    Cambridge
  • Pages/Volumes
    xii, 245 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
Page Top