Davison, Ben Purity of critical cohomology and Kac’s conjecture. (English) Zbl 1419.16010 Math. Res. Lett. 25, No. 2, 469-488 (2018). Summary: We provide a new proof of the Kac positivity conjecture for an arbitrary quiver \(Q\). The ingredients are the cohomological integrality theorem in Donaldson-Thomas theory, dimensional reduction, and an easy purity result. These facts imply the purity of the cohomological Donaldson-Thomas invariants for partially nilpotent representations of a quiver with potential \((\widetilde{Q},W)\) associated to \(Q\), which in turn implies positivity of the Kac polynomials for \(Q\). Cited in 8 Documents MSC: 16G20 Representations of quivers and partially ordered sets 05E10 Combinatorial aspects of representation theory Keywords:Kac positivity conjecture; cohomological Donaldson-Thomas invariants; nilpotent representations PDFBibTeX XMLCite \textit{B. Davison}, Math. Res. Lett. 25, No. 2, 469--488 (2018; Zbl 1419.16010) Full Text: DOI arXiv