ON THE COHOMOLOGY OF TORELLI GROUPS

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 gro...

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Bibliographic Details
Published inForum of mathematics. Pi Vol. 8
Main Authors KUPERS, ALEXANDER, RANDAL-WILLIAMS, OSCAR
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 2020
Subjects
11F75
18D10
20G05
55R40
57S05
Dimensional stability
Homology
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Summary: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.
ISSN:2050-5086
2050-5086
DOI:10.1017/fmp.2020.5