Tropical moduli spaces as symmetric Delta-complexes

Abstract

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.

arXiv comment12 pages. v2: improved exposition, added Remark 6.2 with an alternate proof via geometric group theory that tropical moduli spaces of curves are simply connected, revised title to more fully reflect range of content in paper

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Cited by in corpus (2)

• Tropical trigonal curves
• Stacky fans and tropical moduli in polymake