5 research outputs found
On the Top-Weight Rational Cohomology of
We compute the top-weight rational cohomology of for ,
, and , and we give some vanishing results for the top-weight rational
cohomology of and . When
and , we exhibit nonzero cohomology groups of in odd
degree, thus answering a question highlighted by Grushevsky. Our methods
develop the relationship between the top-weight cohomology of
and the homology of the link of the moduli space of principally polarized
tropical abelian varieties of rank . To compute the latter we use the
Voronoi complexes used by Elbaz-Vincent-Gangl-Soul\'e. Our computations give
natural candidates for compactly supported cohomology classes of
in weight that produce the stable cohomology classes of the
Satake compactification of in weight , under the Gysin
spectral sequence for the latter space.Comment: 33 pages, 3 figure