Papers › A Serre spectral sequence for the moduli space of tropical curves
A Serre spectral sequence for the moduli space of tropical curves
Christin Bibby, Melody Chan, Nir Gadish, Claudia He Yun
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We construct, for all g≥2 and n≥0, a spectral sequence of rational Sₙ-representations which computes the Sₙ-equivariant reduced rational cohomology of the tropical moduli spaces of curves Δ_(g,n) in terms of compactly supported cohomology groups of configuration spaces of n points on graphs of genus g. Using the canonical Sₙ-equivariant isomorphisms Hⁱ⁻¹(Δ_(g,n);ℚ) ≅W₀ Hⁱ_c(ℳ_(g,n);ℚ), we calculate the weight $0$, compactly supported rational cohomology of the moduli spaces ℳ_(g,n) in the range g=3 and n≤9, with partial computations available for n≤13.
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