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We study the topology of moduli spaces of weighted stable tropical curves  Δ g   , w   with fixed genus and unit volume. The space  Δ g   , w   arises as the dual complex of the divisor of singular curves in Hassett’s moduli space M  g   , w   of weighted stable curves. When the genus is positive, we show that  Δ g   , w   is simply connected for any choice of weight vector  w . We also give a formula for the Euler characteristic of  Δ g   , w   in terms of the combinatorics of the weight vector.

Topology of tropical moduli spaces of weighted stable curves in higher genus