Ordering braids / Patrick Dehornoy ; with Ivan Dynnikov, Dale Rolfsen, Bert Wiest.

Format:

Book

Author/Creator:

Dehornoy, Patrick, author.

Dynnikov, Ivan, 1971- author.

Rolfsen, Dale, author.

Wiest, Bert, author.

Series:

Mathematical surveys and monographs ; no. 148.

Mathematical surveys and monographs, 0076-5376 ; volume 148

Language:

English

Subjects (All):

Braid theory.

Linear orderings.

Physical Description:

1 online resource (339 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2008]

Language Note:

English

Summary:

Since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several different approaches have been used to understand this phenomenon. This text provides an account of those approaches, involving varied objects & domains as combinatorial group theory, self-distributive algebra & finite combinatorics.

Contents:

""Contents""; ""Preface""; ""Introduction""; ""Chapter I. Braid Groups""; ""Chapter II. A Linear Ordering of Braid ""; ""Chapter III. Applications of the Braid Ordering""; ""Chapter IV. Self-distributivity""; ""Chapter V. Handle Reduction""; ""Chapter VI. Connection with the Garside Structure""; ""Chapter VII. Alternating Decompositions""; ""Chapter VIII. Dual Braid Monoids""; ""Chapter IX. Automorphisms of a Free Group""; ""Chapter X. Curve Diagrams""; ""Chapter XI. Relaxation Algorithms""; ""Chapter XII. Triangulations""; ""Chapter XIII. Hyperbolic Geometry""

""Chapter XIV. The Space of all Braid Orderings""""Chapter XV. Bi-ordering the Pure Braid Groups""; ""Chapter XVI. Open Questions and Extensions""; ""Key Definitions""; ""Bibliography""; ""Index of Notation""; ""Index""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 311-317) and indexes.

Description based on print version record.

ISBN:

1-4704-1375-2