Seminar

Postdoc day, Seminar 1: Symmetric groups, Hurwitz spaces and moduli spaces of surfaces

Higher algebraic structures in algebra, topology and geometry

11 February 13:30 - 14:00

Andrea Bianchi - University of Copenhagen

Let d=2g>=2 be even. There is a graded commutative Q-algebra, denoted A(d), arising as the conjugation invariants of the associated graded of a multiplicative filtration on the group algebra Q[S_d] of the symmetric group S_d. In joint work with Alexander Christgau and Jonathan Pedersen, I computed a minimal system of generators for A(d) and a formula for the lowest degree relation among minimal generators. There is a simply connected topological space B(d) enjoying the following two properties: -the rational cohomology ring of B(d) is isomorphic to A(d); -a component of the double loop space of B(d) is homotopy equivalent to a component of the group completion of a certain topological monoid Hur(S_d^geo) of Hurwitz spaces. I will briefly describe the topological monoid Hur(S_d^geo) and its relation to the moduli space M_{g,1} of Riemann surfaces of genus g with one boundary curve. Time permitting, I will describe how the lowest degree relation gives rise to a cohomology class in H^{2g-1}(M_{g,1};Q), which I conjecture to be non-trivial.

 

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Organizers
Gregory Arone
Stockholm University
Tilman Bauer
KTH Royal Institute of Technology
Alexander Berglund
Stockholm University
Søren Galatius
University of Copenhagen
Jesper Grodal,
University of Copenhagen
Thomas Kragh
Uppsala University

Program
Contact

Alexander Berglund

alexb@math.su.se

Søren Galatius

galatius@math.ku.dk

Thomas Kragh

thomas.kragh@math.uu.se

Other
information

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