Topological mirror symmetry for rank two character varieties of surface groups

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2021-08-21 DOI:10.1007/s12188-021-00246-y

Mirko Mauri

引用次数: 6

Abstract

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”.

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秩二特征面群的拓扑镜像对称

平坦\（｛\text｛SL｝｝_2\）-和\（｛｛\text｛PGL｝_2｝）-连接的模空间已知为奇异SYZ镜像伙伴。我们建立了它们的交（弦）上同调的Hodge数的相等性。在第二列中，这回答了Tamás Hauser在“Hitchin系统的全局拓扑”的注释3.30中提出的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.