Building on our previous joint work with A. Schmitt, we explain a recursive algorithm to determine the cohomology of moduli spaces of Higgs bundles on any given curve (in the coprime situation). As an application of the method, we compute the -genus of the space of -Higgs bundles for any rank , confirming a conjecture of T. Hausel.
"The -genus of the moduli space of -Higgs bundles on a curve (for degree coprime to )." Duke Math. J. 162 (14) 2731 - 2749, November 2013. https://doi.org/10.1215/00127094-2381369