The y-genus of the moduli space of PGL_n-Higgs bundles on a curve (for   degree coprime to n)
  Building on our previous joint work with A. Schmitt [7] 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 y-genus of the space of PGL_n-Higgs bundles for any rank n, confirming a conjecture of T. Hausel. 
Oscar Garc\'ia-Prada, Jochen Heinloth
math.AG