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We develop techniques for studying fundamental groups and integral singular homology of symmetric Delta-complexes, and apply these techniques to study moduli spaces of stable tropical curves of unit volume, with and without marked points. As one application, we show that Delta_g and Delta_{g,n} are simply connected, for positive g. We also show that Delta_3 is homotopy equivalent to the 5-sphere, and that Delta_4 has 3-torsion in H_5.
We study a space of genus $g$ stable, $n$-marked tropical curves with total edge length $1$. Its rational homology is identified both with top-weight cohomology of the complex moduli space $M_{g,n}$ and with the homology of a marked version of Kontse
We investigate geometric embeddings among several classes of stacky fans and algorithms, e.g., to compute their homology. Interesting cases arise from moduli spaces of tropical curves. Specifically, we study the embedding of the moduli of tropical ho
Let $X$ be a smooth projective curve of genus $g geq 2$ and $M$ be the moduli space of rank 2 stable vector bundles on $X$ whose determinants are isomorphic to a fixed odd degree line bundle $L$. There has been a lot of works studying the moduli and
We use recent results by Bainbridge-Chen-Gendron-Grushevsky-Moeller on compactifications of strata of abelian differentials to give a comprehensive solution to the realizability problem for effective tropical canonical divisors in equicharacteristic
In this paper we prove several lifting theorems for morphisms of tropical curves. We interpret the obstruction to lifting a finite harmonic morphism of augmented metric graphs to a morphism of algebraic curves as the non-vanishing of certain Hurwitz