Cohomology of configuration spaces of surfaces as mapping class group representations
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- by Andreas Stavrou HTML | PDF
- Trans. Amer. Math. Soc. 376 (2023), 2821-2852
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.References
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Additional Information
- Andreas Stavrou
- Affiliation: Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK
- ORCID: 0000-0001-6942-0327
- Email: as2558@cam.ac.uk
- Received by editor(s): September 28, 2021
- Received by editor(s) in revised form: June 17, 2022, and August 19, 2022
- Published electronically: January 12, 2023
- Additional Notes: The author was funded by a studentship of the Engineering and Physical Sciences Research Council (project reference: 2261124)
- © Copyright 2023 by the authors
- Journal: Trans. Amer. Math. Soc. 376 (2023), 2821-2852
- MSC (2020): Primary 55R80, 57R19; Secondary 57K20, 55R20, 55T10, 55R35
- DOI: https://doi.org/10.1090/tran/8804
- MathSciNet review: 4557882