The calculus of braids : an introduction, and beyond / Patrick Dehornoy ; translated by Danièle Gibbons, Greg Gibbons.

Format:

Book

Author/Creator:

Dehornoy, Patrick, author.

Contributor:

Gibbons, Danièle, translator.

Gibbons, Greg, translator.

Series:

London Mathematical Society student texts ; 100.

London Mathematical Society student texts ; 100

Standardized Title:

Calcul des tresses. English.

Language:

English

French

Subjects (All):

Braid theory.

Physical Description:

1 online resource (xii, 245 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

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.

Contents:

Geometric braids

Braid groups

Braid monoids

The greedy normal form

The Artin representation

Handle reduction

The Dynnikov coordinates

A few avenues of investigation

Solutions to the exercises.

Notes:

Title from publisher's bibliographic system (viewed on 01 Sep 2021).

ISBN:

1-108-92288-0

1-108-92112-4

OCLC:

1276856049