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Ordering Braids
Patrick Dehornoy, Université de Caen, France, and Institut Universitaire de France, Paris, France, Ivan Dynnikov, Moscow State University, Russia, Dale Rolfsen, University of British Columbia, Vancouver, BC, Canada, and Bert Wiest, Université de Rennes, France

Mathematical Surveys and Monographs
2008; 323 pp; hardcover
Volume: 148
ISBN-10: 0-8218-4431-8
ISBN-13: 978-0-8218-4431-1
List Price: US$92
Member Price: US$73.60
Order Code: SURV/148
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See also:

Braid and Knot Theory in Dimension Four - Seiichi Kamada

Knots, Braids, and Mapping Class Groups--Papers Dedicated to Joan S. Birman - Jane Gilman, William W Menasco and Xiao-Song Lin

In the fifteen years since the discovery that Artin's braid groups enjoy a left-invariant 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, self-distributive algebra, finite combinatorics, automata, low-dimensional 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 self-contained 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 up-to-date.


Graduate students and research mathematicians interested in braid, group theory, low-dimensional topology.


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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