Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs

Abstract

A conjectural recursive relation for the Poincaré 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.

39 pages; v2: minor changes and references added; v3,v4: some changes in presentation and minor corrections; results unchanged