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Top weight cohomology of moduli spaces of Riemann surfaces and handlebodies
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math.GTmath.AGmath.AT
keywords
cohomologysurfacesclassgrouphandlebodymappingmodulispace
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abstract
We show that a certain locus inside the moduli space $M_g$ 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 $M_g$, studied by Chan-Galatius-Payne, maps injectively into the cohomology of the handlebody mapping class group.
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