Top weight cohomology of moduli spaces of Riemann surfaces and handlebodies

Louis Hainaut; Dan Petersen

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arXiv · 2305.03046

Top weight cohomology of moduli spaces of Riemann surfaces and handlebodies

Louis Hainaut·Dan Petersen

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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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Louis Hainaut, Dan Petersen. 2023-05-04. Top weight cohomology of moduli spaces of Riemann surfaces and handlebodies. https://arxiv.org/abs/2305.03046

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