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ON THE COHOMOLOGY OF TORELLI GROUPS

Part of: Categories with structure Linear algebraic groups and related topics Discontinuous groups and automorphic forms Fiber spaces and bundles

Published online by Cambridge University Press:  13 April 2020

ALEXANDER KUPERS  and
OSCAR RANDAL-WILLIAMS
ALEXANDER KUPERS
Affiliation:
Department of Mathematics, One Oxford Street, Cambridge, MA02138, USA; kupers@math.harvard.edu
OSCAR RANDAL-WILLIAMS
Affiliation:
Centre for Mathematical Sciences, Wilberforce Road, CambridgeCB3 0WB, UK; o.randal-williams@dpmms.cam.ac.uk

Abstract

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We completely describe the algebraic part of the rational cohomology of the Torelli groups of the manifolds $\#^{g}S^{n}\times S^{n}$ relative to a disc in a stable range, for $2n\geqslant 6$. Our calculation is also valid for $2n=2$ assuming that the rational cohomology groups of these Torelli groups are finite-dimensional in a stable range.

MSC classification

Primary: 55R40: Homology of classifying spaces, characteristic classes 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
Secondary: 11F75: Cohomology of arithmetic groups 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories 20G05: Representation theory
Type
Topology
Information
Forum of Mathematics, Pi , Volume 8 , 2020 , e7
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020

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