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Topological mirror symmetry for rank two character varieties of surface groups
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ( IF 0.4 ) Pub Date : 2021-08-21 , DOI: 10.1007/s12188-021-00246-y
Mirko Mauri 1
Affiliation  

The moduli spaces of flat \({\text{SL}}_2\)- and \({\text{PGL}}_2\)-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”.



中文翻译:

面群二阶特征变体的拓扑镜像对称性

已知平面\({\text{SL}}_2\) - 和\({\text{PGL}}_2\) - 连接的模空间是奇异的 SYZ 镜像伙伴。我们建立它们的交集(弦)上同调的霍奇数的相等性。在排名 2 中,这回答了 Tamás Hausel 在“Hitchin 系统的全局拓扑”的备注 3.30 中提出的问题。

更新日期:2021-08-21
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