Synopsis
This is the award-winning monograph of the Sunyer i Balaguer Prize 1999. The book presents 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). Although not a comprehensive course, the exposition is self-contained, and many basic results are established. In particular, the first chapters include a thorough algebraic study of Artin's braid groups.
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Review
"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
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