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braids and self-distributivity (en Inglés)
Dehornoy (Autor)
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Springer
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braids and self-distributivity (en Inglés) - dehornoy
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Reseña del libro "braids and self-distributivity (en Inglés)"
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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