Tropical moduli spaces of stable curves are simply connected, Delta_3 is homotopy equivalent to S^5, and Delta_4 has 3-torsion in H_5 and 2-torsion in H_6 and H_7.
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Tropical moduli spaces as symmetric Delta-complexes
Tropical moduli spaces of stable curves are simply connected, Delta_3 is homotopy equivalent to S^5, and Delta_4 has 3-torsion in H_5 and 2-torsion in H_6 and H_7.