Topological mirror symmetry for rank two character varieties of surface groups
Topological mirror symmetry for rank two character varieties of surface groups
Abstract The moduli spaces of flat $${\text{SL}}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>SL</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> - and $${\text{PGL}}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>PGL</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -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 …