Bonn Topology Group - Abstracts

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Talk

June 25th 2019
Mario Salvetti (Univerisità di Pisa, Italy): Cohomology of superelliptic families and complex braid groups

Abstract

We consider the universal family E_n^d of superelliptic curves: each curve S_n^d in the family is a d-fold covering of the unit disk, totally ramified over a set P of n distinct points; S_n^d --> E_n^d --> Conf_n is a fibre bundle, where Conf_n is the configuration space of n distinct points. We find that E_n^d is the classifying space for the complex braid group of type B(d,d,n) and we compute a big part of the integral homology of E_n^d, including a complete calculation of the stable groups over finite fields by means of Poincare series. The computation of the main part of the above homology reduces to the computation of the homology of the classical braid group with coefficients in the first homology group of S_n^d, endowed with the monodromy action. While giving a geometric description of such monodromy of the above bundle, we introduce generalized 1/d-twists, associated to each standard generator of the braid group, which reduce to standard Dehn twists for d=2.

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