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The present paper is an extension of a previous paper written incollaboration with Markus Reineke dealing with quiver representations. The aimof the paper is to generalize the theory and to provide a comprehensive theoryof Donaldson-Thomas invariants for abelian categories of homological dimensionone (without potential) satisfying some technical conditions. The theory willapply for instance to representations of quivers, coherent sheaves on smoothprojective curves, and some coherent sheaves on smooth projective surfaces. Weshow that the (motivic) Donaldson-Thomas invariants satisfy the Integralityconjecture and identify the Hodge theoretic version with the (compactlysupported) intersection cohomology of the corresponding moduli spaces ofobjects. In fact, we deal with a refined version of Donaldson-Thomas invariantswhich can be interpreted as classes in the Grothendieck group of some "sheaf"on the moduli space. In particular, we reproduce the intersection complex ofmoduli spaces using Donaldson-Thomas theory.

Donaldson-Thomas invariants vs. intersection cohomology for categories of homological dimension one