Topological mirror symmetry for rank two character varieties of surface groups

Abstract

The moduli spaces of flat ${\mathrm{SL}}_2$- and ${\mathrm{PGL}}_2$-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".

7 pages. Comments are welcome!