Tropical moduli spaces as symmetric Δ$\Delta$‐complexes. Issue 1 (5th March 2022) - Allcock, Daniel
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 $H_5$ .