Hardcover ISBN:  9780821844311 
Product Code:  SURV/148 
323 pp 
List Price:  $103.00 
MAA Member Price:  $92.70 
AMS Member Price:  $82.40 
Electronic ISBN:  9781470413750 
Product Code:  SURV/148.E 
323 pp 
List Price:  $97.00 
MAA Member Price:  $87.30 
AMS Member Price:  $77.60 

Book DetailsMathematical Surveys and MonographsVolume: 148; 2008MSC: Primary 20; Secondary 06; 57; 68;
In the fifteen years since the discovery that Artin's braid groups enjoy a leftinvariant linear ordering, several quite different approaches have been used to understand this phenomenon. This book is an account of those approaches, which involve such varied objects and domains as combinatorial group theory, selfdistributive algebra, finite combinatorics, automata, lowdimensional topology, mapping class groups, and hyperbolic geometry. The remarkable point is that all these approaches lead to the same ordering, making the latter rather canonical.
We have attempted to make the ideas in this volume accessible and interesting to students and seasoned professionals alike. Although the text touches upon many different areas, we only assume that the reader has some basic background in group theory and topology, and we include detailed introductions wherever they may be needed, so as to make the book as selfcontained as possible.
The present volume follows the book, Why are braids orderable?, written by the same authors and published in 2002 by the Société Mathématique de France. The current text contains a considerable amount of new material, including ideas that were unknown in 2002. In addition, much of the original text has been completely rewritten, with a view to making it more readable and uptodate.ReadershipGraduate students and research mathematicians interested in braid, group theory, lowdimensional topology.

Table of Contents

Chapters

Introduction

1. Braid groups

2. A linear ordering of braids

3. Applications of the braid ordering

4. Selfdistributivity

5. Handle reduction

6. Connection with the Garside structure

7. Alternating decompositions

8. Dual braid monoids

9. Automorphisms of a free group

10. Curve diagrams

11. Relaxation algorithms

12. Triangulations

13. Hyperbolic geometry

14. The space of all braid orderings

15. Biordering the pure braid groups

16. Open questions and extensions


Additional Material

Reviews

From a review of the previous edition: ...this is a timely and very carefully written book describing important, interesting and beautiful results in this new area of research concerning braid groups. It will no doubt create much interest and inspire many more insights into these order structures.
Stephen P. Humphries for Mathematical Reviews


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In the fifteen years since the discovery that Artin's braid groups enjoy a leftinvariant linear ordering, several quite different approaches have been used to understand this phenomenon. This book is an account of those approaches, which involve such varied objects and domains as combinatorial group theory, selfdistributive algebra, finite combinatorics, automata, lowdimensional topology, mapping class groups, and hyperbolic geometry. The remarkable point is that all these approaches lead to the same ordering, making the latter rather canonical.
We have attempted to make the ideas in this volume accessible and interesting to students and seasoned professionals alike. Although the text touches upon many different areas, we only assume that the reader has some basic background in group theory and topology, and we include detailed introductions wherever they may be needed, so as to make the book as selfcontained as possible.
The present volume follows the book, Why are braids orderable?, written by the same authors and published in 2002 by the Société Mathématique de France. The current text contains a considerable amount of new material, including ideas that were unknown in 2002. In addition, much of the original text has been completely rewritten, with a view to making it more readable and uptodate.
Graduate students and research mathematicians interested in braid, group theory, lowdimensional topology.

Chapters

Introduction

1. Braid groups

2. A linear ordering of braids

3. Applications of the braid ordering

4. Selfdistributivity

5. Handle reduction

6. Connection with the Garside structure

7. Alternating decompositions

8. Dual braid monoids

9. Automorphisms of a free group

10. Curve diagrams

11. Relaxation algorithms

12. Triangulations

13. Hyperbolic geometry

14. The space of all braid orderings

15. Biordering the pure braid groups

16. Open questions and extensions

From a review of the previous edition: ...this is a timely and very carefully written book describing important, interesting and beautiful results in this new area of research concerning braid groups. It will no doubt create much interest and inspire many more insights into these order structures.
Stephen P. Humphries for Mathematical Reviews