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SUMMARY:Cohomology of Torelli groups - Oscar Randal-Williams\, Cambridge
DTSTART:20190313T160000Z
DTEND:20190313T170000Z
UID:TALK121120@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:It is a basic problem in the cohomology of moduli spaces of Ri
 emann surfaces to describe the cohomology of the Torelli group---the subgr
 oup of the mapping class group of those diffeomorphisms which act triviall
 y 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. Thi
 s question can be generalised to higher dimensions by replacing the genus 
 g surface with its analogue #^g S^n 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 fini
 teness conjecture about the cohomology of this Torelli group.
LOCATION:MR13
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