Monodromy representations of braid groups

The group Bn of braids on n strands is the fundamental group of the configuration space of n points in the plane. Thus, by considering some fiber bundle over the configuration space and taking the corresponding monodromy homomorphism, one obtains a representation of Bn. In this talk we discuss the following representations, treating each of them as a monodromy homomorphism:

  1. Artin representation.
  2. Burau representation.
  3. Lawrence-Krammer-Bigelow representation (a faithful linear representation of Bn, by a recent result) and, if the time permits,
  4. Chen's iterated integral of a canonical formal power series connection, which is the same thing as Kontsevich integral for braids.

Ivan Izmestiev

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