Cohomology of configuration spaces of surfaces as mapping class group representations
Algebraic Topology
2021-07-20 v1
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.
Keywords
Cite
@article{arxiv.2107.08462,
title = {Cohomology of configuration spaces of surfaces as mapping class group representations},
author = {Andreas Stavrou},
journal= {arXiv preprint arXiv:2107.08462},
year = {2021}
}