糖果派对

Speaker: Oscar Bendix Harr (University of Copenhagen) [nl][nl]
Abstract:[nl] Not much is known about the cohomology of the moduli space of handlebodies (equivalently, the cohomology of handlebody mapping class groups) except what it stabilizes to, by Hatcher's analogue of the Madsen--Weiss theorem. Hatcher and Wahl have shown that the degree d cohomology of the moduli space of genus g handlebodies is stable for d less than roughly g/2. I will discuss some work from my PhD thesis (in preparation) which expands this range to g roughly less than 2g/3, using the methods of Galatius, Kupers, and Randal-Williams. By a computation of Morita, this is the optimal range for homological stability for moduli spaces of handlebody groups. A similar argument shows that the cohomology of automorphism groups of free groups Aut(F_n) is stable in degrees roughly less than 2n/3, which improves the best known range for integer coefficients. Time provided, I will also say something about ongoing work on the cohomology outside the stable range.
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