Filtrations of moduli spaces of tropical weighted stable curves

Abstract

We study how changing the weight datum A = (a 1 , ..., a n ) ∈ (Q ∩ (0, 1]) n affects the topology of tropical moduli spaces M trop g,A , M trop g,A and ∆ g,A and the homology of the latter one. We show that for fixed g and n, there are particular filtrations of these topological spaces which we can use to compute the reduced rational homology of ∆ g,A and the top weight cohomology of the moduli space M g,A of smooth (g, A)-stable algebraic curves.

Automorphisms of tropical Hassett spaces

“…Closed formulas for the number of spheres are known when w is heavy/light. In higher genus, the topology of g;w has been explored by Li, Serpente, Yun, and the third author in [19], and by Serpente in [27]. When g 1, and for any value of w, the space g;w is shown to be simply-connected.…”