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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Topology

• Full title: Braids and Self-Distributivity
• Author: Patrick Dehornoy
• Language: English
• Binding: Hardback
• Number of pages: 623
• EAN: 9783764363437
• ISBN: 3764363436
• ID: 01716488
• Publisher: Birkhauser Verlag AG
• Weight: 2390 g
• Dimensions: 235 × 155 × 39 mm
• Date of publishing: 01. July 2000

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