Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

Abstract

For G = GL2; PGL2; SL2 we prove that the perverse ltration associated with the Hitchin map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a compact Riemann surface C agrees with the weight ltration on the rational cohomology of the twisted G character variety of C when the cohomologies are identied via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves.