Moduli spaces of tropical curves of higher genus with marked points and homotopy colimits

Abstract

The main characters of this paper are the moduli spaces TMg,n of tropical curves of genus g with n marked points, with g ≥ 2. We reduce the study of the homotopy type of these spaces to the analysis of compact spaces Xg,n, which in turn possess natural representations as homotopy colimits of diagrams of topological spaces over combinatorially defined generalized simplicial complexes Δg, with the latter being interesting on their own right.