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Why Are Braids Orderable?
Patrick Dehornoy, Université de Caen, France, Ivan Dynnikov, Moscow State University, Russia, Dale Rolfsen, University of British Columbia, Vancouver, BC, Canada, and Bert Wiest, Université de Rennes I, France
A publication of the Société Mathématique de France.
Panoramas et Synthèses
2002; 190 pp; softcover
Number: 14
ISBN-10: 2-85629-135-X
ISBN-13: 978-2-85629-135-1
List Price: US$33
Member Price: US$26.40
Order Code: PASY/14
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In the decade since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several quite different approaches have been applied to understand this phenomenon. This book is an account of those approaches, involving self-distributive algebra, uniform finite trees, combinatorial group theory, mapping class groups, laminations, and hyperbolic geometry.

This volume is suitable for graduate students and research mathematicians interested in algebra and topology.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in algebra and topology.

Table of Contents

  • A linear ordering of braids
  • Self-distributivity
  • Handle reduction
  • Finite trees
  • Automorphisms of a free group
  • Curve diagrams
  • Hyperbolic geometry
  • Triangulations
  • Bi-ordering the pure braid groups
  • Open questions
  • Bibliography
  • Index
  • Index of notation
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