Wallcrossing and cohomology of the moduli space of Hitchin pairs

Abstract

A conjectural recursive relation for the Poincaŕe polynomial of the Hitchin moduli space is derived from wallcrossing in the refined local Donaldson-Thomas theory of a curve. A doubly refined generalization of this theory is also conjectured and shown to similarly determine the Hodge polynomial of the same moduli space.