Top weight cohomology of moduli spaces of Riemann surfaces and handlebodies

• DOI: 10.4171/jems/1623
• Publication Date: 2025-03-10T12:01:27Z
• Authors: Louis Hainaut; Dan Petersen

We show that a certain locus inside the moduli space

\mathcal{M}_{g}

of hyperbolic surfaces, given by surfaces with “sufficiently many” short geodesics, is a classifying space of the handlebody mapping class group. A consequence of the construction is that the top weight cohomology of

\mathcal{M}_{g}

, studied by Chan–Galatius–Payne, maps injectively into the cohomology of the handlebody mapping class group.