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

Abstract

We study the topology of moduli spaces of weighted stable tropical curves Δg ,w with fixed genus and unit volume. The space Δg ,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 Δg ,w is simply connected for any choice of weight vector w. We also give a formula for the Euler characteristic of Δg ,w in terms of the combinatorics of the weight vector.