CRM: Centro De Giorgi
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Arrangements and beyond: Combinatorics, geometry, topology and applications

Cohomology of Configuration Spaces and Artin groups: applications

speaker: Mario Salvetti (Dipartimento di Matematica, Università di Pisa)

abstract: Several (topologically and combinatorially based) methods for the cohomology of Artin groups were previously developed. As an application to a geometric situation which is of a very wide interest, we completely calculate the integral (co)homology of the so called hyperelliptic locus, namely the space $En$ of genus $g$ curves ramified over $n=2g+1$ points. The main part of such (co)homology is described by the (co)homology of the braid group with coefficients in a symplectic representation, namely the braid group acts on the first homology group of a genus $g$ surface in a standard way. Our computations confirm some previous experimental results, showing that such groups have only $2-$torsion. We also find the Poincar\'e series for the (co)homology, in particular the series for the stable groups (joint work with F. Callegaro).

Thu 8 Jun, 10:50 - 11:30, Aula Dini
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