Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariants

Abstract

A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert-scheme-type) framed versions of quiver moduli is derived. This is applied to wall-crossing formulas for the Donaldson-Thomas type invariants of M. Kontsevich and Y. Soibelman, in particular confirming their integrality. © Copyright Foundation Compositio Mathematica 2011.