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Braids and Self-Distributivity (Progress in Mathematics) [Hardcover]

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Item description for Braids and Self-Distributivity (Progress in Mathematics) by Patrick Dehornoy...

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.
In the 1980s new examples of left self-distributive systems were discovered using unprovable axioms of set theory, and purely algebraic statements were deduced. The quest for elementary proofs of these statements led to a general theory of self-distributivity centered on a certain group that captures the geometrical properties of this identity. This group happens to be closely connected with Artin's braid groups, and new properties of the braids naturally arose as an application, in particular the existence of a left invariant linear order, which subsequently received alternative topological constructions.
The text proposes a first synthesis of this area of research. Three domains are considered here, namely braids, self-distributive systems, and set theory. Although not a comprehensive course on these subjects, the exposition is self-contained, and a number of basic results are established. In particular, the first chapters include a rather complete algebraic study of Artin's braid groups.

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Item Specifications...

Pages   623
Est. Packaging Dimensions:   Length: 9.3" Width: 6.3" Height: 1.5"
Weight:   2.65 lbs.
Binding  Hardcover
Release Date   Sep 6, 2000
Publisher   Birkhäuser Basel
ISBN  3764363436  
ISBN13  9783764363437  

Availability  122 units.
Availability accurate as of Oct 25, 2016 01:55.
Usually ships within one to two business days from La Vergne, TN.
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Product Categories

1Books > Subjects > Medicine > General
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Geometry & Topology > Algebraic Geometry
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Set Theory
4Books > Subjects > Science > General
5Books > Subjects > Science > Mathematics > General
6Books > Subjects > Science > Mathematics > Geometry & Topology > Algebraic Geometry
7Books > Subjects > Science > Mathematics > Geometry & Topology > Topology
8Books > Subjects > Science > Mathematics > Pure Mathematics > Set Theory

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