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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Cohomology of Torelli groups - Oscar Randal-Willia
ms\, Cambridge
DTSTART;TZID=Europe/London:20190313T160000
DTEND;TZID=Europe/London:20190313T170000
UID:TALK121120AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/121120
DESCRIPTION:It is a basic problem in the cohomology of moduli
spaces of Riemann surfaces to describe the cohomol
ogy of the Torelli group---the subgroup of the map
ping class group of those diffeomorphisms which ac
t 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 surf
ace. This question can be generalised to higher di
mensions 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 que
stion 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.
LOCATION:MR13
CONTACT:Ivan Smith
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