Topological mirror symmetry for rank two character varieties of surface groups

Topological mirror symmetry for rank two character varieties of surface groups

The moduli spaces of flat SL 2 - and PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin s...

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Veröffentlicht in:Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2021-10, Vol.91 (2), p.297-303
1. Verfasser: Mauri, Mirko
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Algebra
Differential Geometry
Geometry
Homology
Mathematics
Mathematics and Statistics
Number Theory
Topology
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description The moduli spaces of flat SL 2 - and PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.
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subjects Algebra
Differential Geometry
Geometry
Homology
Mathematics
Mathematics and Statistics
Number Theory
Topology
title Topological mirror symmetry for rank two character varieties of surface groups
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