Configuration Spaces: Geometry, Combinatorics and Topology

YOUNG SEMINAR: Symmetric group actions on the cohomology of configuration spaces

speaker: Giacomo d'Antonio (University of Bremen)

abstract: The symmetric group S_n acts in a natural way on the configuration space F(M,n) of a manifold M and thus on its cohomology algebra H(F(M,n); ℂ). We will approach this topic with representation-theoretic methods, focusing on the cases M = ℝ^k and M = S^k of euclidean spaces and spheres. The first case can be worked out introducing an auxiliary extended action of S_n+1 on the algebra H(F(ℝ^k,n); ℂ), thus allowing some sort of recursive argument. This extended action turns out to be one of the building blocks of the action of S_n+1 on the cohomology H(F(S^k, n+1); ℂ) of the configuration space of spheres.

timetable:
Fri 28 May, 17:00 - 18:00, Sala Conferenze Centro De Giorgi
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