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Cohomology of configuration spaces of surfaces as mapping class group representations

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Peer-reviewed

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Authors

Stavrou, Andreas 

Abstract

We express the rational cohomology of the unordered configuration space of a compact oriented manifold as a representation of its mapping class group in terms of a weight-decomposition of the rational cohomology of the mapping space from the manifold to a sphere. We apply this to the case of a compact oriented surface with one boundary component and explicitly compute the rational cohomology of its unordered configuration space as a representation of its mapping class group. In particular, this representation is not symplectic, but has trivial action of the second Johnson filtration subgroup of the mapping class group.

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Journal Title

Transactions of the American Mathematical Society

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Journal ISSN

0002-9947

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Publisher

American Mathematical Society

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Sponsorship
Engineering and Physical Sciences Research Council (2261124)