On the top-weight rational cohomology of 𝒜g

We compute the top-weight rational cohomology of A g for g D 5, 6 and 7, and we give some vanishing results for the top-weight rational cohomology of A 8 ; A 9 and A 10 .When g D 5 and g D 7, we exhibit nonzero cohomology groups of A g in odd degree, thus answering a question highlighted by Grushevsky.Our methods develop the relationship between the top-weight cohomology of A g and the homology of the link of the moduli space of principally polarized tropical abelian varieties of rank g.To compute the latter we use the Voronoi complexes used by Elbaz-Vincent, Gangl and Soulé.In this way, our results make a precise connection between the rational cohomology of Sp 2g .Z/ and GL g .Z/.Our computations also give natural candidates for compactly supported cohomology classes of A g in weight 0 that produce the stable cohomology classes of the Satake compactification of A g in weight 0, under the Gysin spectral sequence for the latter space.