The tropicalization of the moduli space of curves II: Topology and   applications
  We study the topology of the tropical moduli space parametrizing stable tropical curves of genus g with n marked points in which the bounded edges have total length 1, and prove that it is highly connected. Using the identification of this space with the dual complex of the boundary in the moduli space of stable algebraic curves, we give a simple expression for the top weight cohomology of M_{1,n} as a representation of the symmetric group and describe an explicit dual basis in homology consisting of abelian cycles for the pure mapping class group. 
Melody Chan, Soren Galatius, Sam Payne
math.AG math.CO math.GT