Abstract

Braid groups have a representation theory of wild type, in the sense that there is no known classification schema. Hence it is useful to shape constructions of linear representations for such family of groups to understand its representation theory. For this purpose, Lawrence and Bigelow constructed representations of the braid group on n strands using the configuration space of m points of a n-punctured disc: namely, the braid group acts on the m-th homology group of a particular covering of the configuration space. There is actually an underlying general method to build such homological representations.

In this talk, I will present a unified functorial approach to this method for general families of groups. I will also show that, under some additional assumptions, general notions of polynomiality on functors are a useful tool to classify these representations. This is a joint work with Martin Palmer.