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The aim of this paper is to study an analog of non-commutativeDonaldson-Thomas theory corresponding to the refined topological vertex forsmall crepant resolutions of toric Calabi-Yau 3-folds. We define the invariantsusing dimer models and provide "wall-crossing" formulas. In particular, we getnormalized generating functions which are unchanged under "wall-crossing".

Refined open non-commutative Donaldson-Thomas invariants for small crepant resolutions