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Introduction to representations of braid groups

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arxiv 1404.0724 v1 pith:N57JA3HE submitted 2014-04-02 math.AT math.QA

Camilo Arias Abad This is my paper · ORCID
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These are lecture notes prepared for a minicourse given at the Cimpa Research School "Algebraic and geometric aspects of representation theory", held in Curitiba, Brazil in March 2013. The purpose of the course is to provide an introduction to the study of representations of braid groups. Three general classes of representations of braid groups are considered: homological representations via mapping class groups, monodromy representations via the Knizhnik-Zamolodchikov connection, and solutions of the Yang-Baxter equation via braided bialgebras. Some of the remarkable relations between these three different constructions are described.

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    Fractional quantum Hall anyons are re-derived from a non-Lagrangian flux quantization in 2-Cohomotopy, with new predictions for torus degeneracy and defect anyons.

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