Torelli group action on the configuration space of a surface

Eduard Looijenga

doi:10.1142/S1793525321500370

Torelli group action on the configuration space of a surface

Eduard Looijenga^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We show that the Torelli group of a closed surface of genus ≥ 3 acts nontrivially on the rational cohomology of the space of 3-element subsets of that surface. This implies that for a Riemann surface of genus ≥ 3, the mixed Hodge structure on the space of its positive, reduced divisors of degree 3 does in general not split over Q.

Original language	English
Pages (from-to)	215-222
Number of pages	8
Journal	Journal of Topology and Analysis
Volume	15
Issue number	1
Early online date	2021
DOIs	https://doi.org/10.1142/S1793525321500370
Publication status	Published - 1 Mar 2023

Keywords

Configuration space
Torelli group
mixed Hodge structure

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10.1142/S1793525321500370

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abstract = "We show that the Torelli group of a closed surface of genus ≥ 3 acts nontrivially on the rational cohomology of the space of 3-element subsets of that surface. This implies that for a Riemann surface of genus ≥ 3, the mixed Hodge structure on the space of its positive, reduced divisors of degree 3 does in general not split over Q.",

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AB - We show that the Torelli group of a closed surface of genus ≥ 3 acts nontrivially on the rational cohomology of the space of 3-element subsets of that surface. This implies that for a Riemann surface of genus ≥ 3, the mixed Hodge structure on the space of its positive, reduced divisors of degree 3 does in general not split over Q.

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Torelli group action on the configuration space of a surface

Abstract

Keywords

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