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Braids and Self-Distributivity (Hardcover, 2000 ed.)
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Braids and Self-Distributivity (Hardcover, 2000 ed.)
Series: Progress in Mathematics, 192
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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."
General
Imprint: |
Birkhauser Verlag AG
|
Country of origin: |
Switzerland |
Series: |
Progress in Mathematics, 192 |
Release date: |
July 2000 |
First published: |
2000 |
Authors: |
Patrick Dehornoy
|
Dimensions: |
235 x 155 x 35mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
623 |
Edition: |
2000 ed. |
ISBN-13: |
978-3-7643-6343-7 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
General
|
LSN: |
3-7643-6343-6 |
Barcode: |
9783764363437 |
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