Lawrence representations of braid groups: a self-distributive approach

Victoria Lebed (Dublin)

Monday 15th January, 2018 16:00-17:00 Maths 311B


Long and Moody developed an ingenious procedure for transforming  a representation of the braid group B_{n+1} into a more sophisticatedrepresentation of B_n. For instance, the trivial representation is upgraded to the Burau representation, which in its turn yields the Lawrence-Krammer-Bigelow one. Topological and algebraic versions of this procedure are known, the last one vastly generalised by Bigelow and Tian. In this talk we shall present a new, combinatorial avatar of the Bigelow-Tian construction, and discuss its applications. Our interpretation is based on an enhanced version of quandles (certain sets with a self-distributive binary operation).

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