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:

xii, 245 pages ; 24 cm.

Place of Publication:

Cambridge ; New York, NY : 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 at all evident that we can construct a theory about them, that is, elaborate a coherent and mathematically interesting corpus of results concerning them. Our goal here is to convince the reader that there is a resoundingly positive response to this question: braids are indeed fascinating objects, with a variety of rich mathematical properties. For this, we will concentrate on carefully and completely establishing only a few selected results. What they have in common is the sophistication of the proofs they require, in spite of their very simple statements. At the heart of the approach, a natural multiplication operation of braids leads to group structures, the braid groups. Combining both algebraic and topological aspects, these groups enjoy multiple interesting properties and are at the same time simple and complex"-- Provided by publisher.

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:

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

Includes bibliographical references and index.

Other Format:

Online version: Dehornoy, Patrick. Calcul des tresses. English Calculus of braids

ISBN:

9781108843942

1108843948

OCLC:

1263247293