Title: On the topology of the moduli space of tropical Z/pZ-covers
Abstract: 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. We prove contractibility of certain subcomplexes of the tropical moduli space and use this result to show that it is simply connected and to fully determine its homotopy type for g=2 and all p.