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Cohomology of Torelli groups

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  • UserOscar Randal-Williams, Cambridge
  • ClockWednesday 13 March 2019, 16:00-17:00
  • HouseMR13.

If you have a question about this talk, please contact Ivan Smith.

It is a basic problem in the cohomology of moduli spaces of Riemann surfaces to describe the cohomology of the Torelli group—-the subgroup of the mapping class group of those diffeomorphisms which act trivially on the first cohomology of the surface—-as a representation of Sp(2g, Z), at least in a stable range depending on the genus of the surface. This question can be generalised to higher dimensions by replacing the genus g surface with its analogue #g Sn x S^n. I will present joint work with Alexander Kupers in which we answer this question in dimensions at least 6. Our description is also valid in the classical case 2n=2 assuming a finiteness conjecture about the cohomology of this Torelli group.

This talk is part of the Differential Geometry and Topology Seminar series.

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