The orbifold topological vertex

We develop a topological vertex formalism for computing the Donaldson–Thomas invariants of Calabi–Yau orbifolds. The basic combinatorial object is the orbifold vertex , a generating function for the number of 3D partitions asymptotic to 2D partitions λ, μ, ν and colored by representations of a finite Abelian group G acting on C3. In the case where G≅Zn acting on C3 with transverse An−1 quotient singularities, we give an explicit formula for in terms of Schur functions. We discuss applications of our formalism to the Donaldson–Thomas crepant resolution conjecture and to the orbifold Donaldson–Thomas/Gromov–Witten correspondence. We also explicitly compute the Donaldson–Thomas partition function for some simple orbifold geometries: the local football and the local BZ2 gerbe.