Topological mirror symmetry for parabolic Higgs bundles

Abstract

We prove the topological mirror symmetry conjecture of Hausel–Thaddeus (Hausel and Thaddeus, 2001, 2003) for the moduli space of strongly parabolic Higgs bundles of rank two and three, with full flags, for any generic weights. Although the main theorem is proved only for rank at most three, most of the results are proved for any prime rank.