Ordering braids
by Patrick Dehornoy , Ivan Dynnikov , Dale Rolfsen , and Bert Wiest

Persian Title: نوارهای چیدمان

Summary and Info
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 Societe Mathematique 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
More About the Author
Patrick Dehornoy (born September 11, 1952 in Rouen) is a mathematician at the University of Caen who works on set theory and algebra.
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