Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariants
Markus Reineke
TL;DR
This paper derives functional equations connecting Euler characteristics of quiver moduli spaces and their framed variants, applying these to wall-crossing formulas for Donaldson-Thomas invariants and confirming their integrality.
Contribution
It introduces a system of functional equations linking different Euler characteristics and applies them to prove the integrality of Donaldson-Thomas invariants.
Findings
Functional equations relate Euler characteristics of quiver moduli spaces.
Confirmed the integrality of Donaldson-Thomas invariants.
Applied wall-crossing formulas to quiver moduli.
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.
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