Tropical moduli spaces as symmetric Δ$\Delta$‐complexes
Daniel Allcock, Daniel Corey, Sam Payne
Abstract
We develop techniques for studying fundamental groups and integral singular homology of symmetric Δ $\Delta$ -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 Δ g $\Delta _g$ and Δ g , n $\Delta _{g,n}$ are simply connected, for g ⩾ 1 $g \geqslant 1$ . We also show that Δ 3 $\Delta _3$ is homotopy equivalent to the 5-sphere, and that Δ 4 $\Delta _4$ has 3-torsion in H 5 $H_5$ .
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