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

Abstract

For G = GL_2, PGL_2 and SL_2 we prove that the perverse filtration associated to the Hitchin map on the cohomology of the moduli space of twisted G-Higgs bundles on a Riemann surface C agrees with the weight filtration on the cohomology of the twisted G character variety of C, when the cohomologies are identified 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.

67 pages, arguments streamlined, to appear in Annals of Mathematics

References in corpus (2)

• Global topology of the Hitchin system
• On the E-polynomials of a family of Character Varieties

Cited by in corpus (8)

• Global topology of the Hitchin system
• Cell decompositions of character varieties
• Cohomology of large semiprojective hyperkaehler varieties
• BPS states and the P=W conjecture
• Hitchin Fibrations on Two-Dimensional Moduli Spaces of Irregular Higgs Bundles with One Singular Fiber
• Twisted spectral correspondence and torus knots
• Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus
• Families of Hitchin systems and N=2 theories