Título: On the topology of the moduli space of tropical Z/pZ-covers

Palestrante: Pedro Souza (Universität Frankfurt)

 

Resumo:

 

We study the topology of the moduli space of (unramified) Z/pZ-covers of tropical curves of genus g≥2 where p is a prime number.
By recent work of Chan-Galatius-Payne, the (reduced) homology of this tropical moduli space computes (with a degree-shift)
the top-weight (rational) cohomology of the corresponding algebraic  moduli space.
This approach gives new geometric techniques for understanding the group cohomology of the mapping class group of a surface of genus g.
We investigate the algebraic topology of this tropical moduli space and use the result to show that
it is simply connected and to fully determine its homotopy type for g=2 and all primes p.