Progress in Mathematics

Braids and Self-Distributivity

Authors: Dehornoy, Patrick

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About this book

The aim of this book is to present recently discovered connections between Artin's braid groups En and left self-distributive systems (also called LD­ systems), which are sets equipped with a binary operation satisfying the left self-distributivity identity x(yz) = (xy)(xz). (LD) Such connections appeared in set theory in the 1980s and led to the discovery in 1991 of a left invariant linear order on the braid groups. Braids and self-distributivity have been studied for a long time. Braid groups were introduced in the 1930s by E. Artin, and they have played an increas­ ing role in mathematics in view of their connection with many fields, such as knot theory, algebraic combinatorics, quantum groups and the Yang-Baxter equation, etc. LD-systems have also been considered for several decades: early examples are mentioned in the beginning of the 20th century, and the first general results can be traced back to Belousov in the 1960s. The existence of a connection between braids and left self-distributivity has been observed and used in low dimensional topology for more than twenty years, in particular in work by Joyce, Brieskorn, Kauffman and their students. Brieskorn mentions that the connection is already implicit in (Hurwitz 1891). The results we shall concentrate on here rely on a new approach developed in the late 1980s and originating from set theory.

Reviews

"In this book…P. Dehornoy has accomplished with remarkable success the task of presenting the area of interaction where Artin’s braid groups, left self-distributive systems (LD-systems) and set theory come together in a rigorous and clear manner…The exposition is self-contained and there are no prerequisites. A number of basic results about braid groups, self-distributive algebras, and set theory are provided."

--Mathematical Reviews


Table of contents (13 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-8442-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-7643-6343-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-9568-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Braids and Self-Distributivity
Authors
Series Title
Progress in Mathematics
Series Volume
192
Copyright
2000
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8442-6
DOI
10.1007/978-3-0348-8442-6
Hardcover ISBN
978-3-7643-6343-7
Softcover ISBN
978-3-0348-9568-2
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIX, 623
Topics