The topology of moduli spaces of tropical curves with marked points
The author studies the topology of moduli spaces of tropical curves of genus \(g\) with \(n\) marked points. He considers the moduli spaces as being embedded in a larger space called the moduli space of metric graphs with \(n\) marked points, and he describes the shrinking bridges strong deformation retraction, which leads to a substantial simplification of all these moduli spaces. In particular, he studies the case \(g=1\) carefully and he shows that the corresponding moduli space is presented as a quotient space of torus with respect to the conjugation \(\mathbb Z_2\)-action. As its application, he also computes the all Betti numbers of \(\mathbb Z_2\) coefficients for this moduli space.
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