  The present paper is an extension of a previous paper written in
collaboration with Markus Reineke dealing with quiver representations. The aim
of the paper is to generalize the theory and to provide a comprehensive theory
of Donaldson-Thomas invariants for abelian categories of homological dimension
one (without potential) satisfying some technical conditions. The theory will
apply for instance to representations of quivers, coherent sheaves on smooth
projective curves, and some coherent sheaves on smooth projective surfaces. We
show that the (motivic) Donaldson-Thomas invariants satisfy the Integrality
conjecture and identify the Hodge theoretic version with the (compactly
supported) intersection cohomology of the corresponding moduli spaces of
objects. In fact, we deal with a refined version of Donaldson-Thomas invariants
which can be interpreted as classes in the Grothendieck group of some "sheaf"
on the moduli space. In particular, we reproduce the intersection complex of
moduli spaces using Donaldson-Thomas theory.
