Braids and Self-Distributivity 2000 Edition Contributor(s): Dehornoy, Patrick (Author) |
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ISBN: 3764363436 ISBN-13: 9783764363437 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: July 2000 Annotation: This is the award-winning monograph of the Sunyer i Balaguer Prize 1999. The aim of this book is to present recently discovered connections between Artin's braid groups and left self-distributive systems, which are sets equipped with a binary operation satisfying the identity x(yz) = (xy)(xz). Order properties are crucial. |
Additional Information |
BISAC Categories: - Mathematics | Topology - General - Medical |
Dewey: 514.224 |
LCCN: 00-44488 |
Series: Erganzungsbande Zu Den Tituli Asiae Minoris |
Physical Information: 1.38" H x 6.14" W x 9.21" (2.38 lbs) 623 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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. |