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Mapping class group actions on the cohomology of configuration spaces of surfaces

  • Clément Dupont
  • Richard Hain
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Abstract

Let X be a closed oriented surface of genus at least 2 and P a finite subset of X. We bound the action of the mapping class group of (X,P) on the rational cohomology groups of the ordered configuration spaces F_n(X-P) of X-P. In particular, we show that, when #P < 2, the diagonal action of the mapping class group on the direct sum of the H^n(F_n(X-P)) is faithful, and determine its kernel when #P > 1.

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Cite

BibTeXRIS
BibTeX
@misc{dupont2026mapping,
  title = {{Mapping class group actions on the cohomology of configuration spaces of surfaces}},
  author = {Clément Dupont and Richard Hain},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05126},
  eprint = {2611.05126},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05126},
}
RIS
TY  - UNPB
TI  - Mapping class group actions on the cohomology of configuration spaces of surfaces
AU  - Clément Dupont
AU  - Richard Hain
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05126
UR  - https://arxiv.org/abs/2611.05126
AB  - Let X be a closed oriented surface of genus at least 2 and P a finite subset of X. We bound the action of the mapping class group of (X,P) on the rational cohomology groups of the ordered configuration spaces F_n(X-P) of X-P. In particular, we show that, when #P < 2, the diagonal action of the mapping class group on the direct sum of the H^n(F_n(X-P)) is faithful, and determine its kernel when #P > 1.
ER  -