Geodesic
Extra structure on the cohomology of configuration spaces of closed orientable surfaces
Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 127-146.

Voir la notice de l'article provenant de la source International Press of Boston

The rational homology of unordered configuration spaces of points on any surface was studied by Drummond–Cole and Knudsen. We compute the rational cohomology of configuration spaces on a closed orientable surface, keeping track of the mixed Hodge numbers and the action of the symplectic group on the cohomology. We find a series with coefficients in the Grothendieck ring of $\mathfrak{sp}(2g)$ that describes explicitly the decomposition of the cohomology into irreducible representations. From that we deduce the mixed Hodge numbers and the Betti numbers, obtaining a new formula without cancellations.
DOI : 10.4310/HHA.2023.v25.n1.a7
Classification : 55R80
Keywords: configuration space, surface, cohomology 
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     author = {Roberto Pagaria},
     title = {Extra structure on the cohomology of configuration spaces of closed orientable surfaces},
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     pages = {127--146},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a7/}
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Roberto Pagaria. Extra structure on the cohomology of configuration spaces of closed orientable surfaces. Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 127-146. doi : 10.4310/HHA.2023.v25.n1.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a7/

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