The Topology of Moduli Spaces of Tropical Curves with Marked Points
Dmitry N. Kozlov · Asian Journal of Mathematics · 2009
In this paper we study the topology of moduli spaces of tropical curves of genus g with n marked points.We view the moduli spaces as being embedded in a larger space, which we call the moduli space of metric graphs with n marked points.We describe the shrinking bridges strong deformation retraction, which leads to a substantial simplification of all these moduli spaces.In the rest of the paper, this reduction is used to analyze the case of genus 1.The corresponding moduli space is presented as a quotient space of a torus with respect to the conjugation Z 2 -action; and furthermore, as a homotopy colimit over a simple diagram.The latter allows us to compute all Betti numbers of this moduli space with coefficients in Z 2 .