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We define a formalism for computing open orbifold GW invariants of [C^3/G]where G is any finite abelian group. We prove that this formalism and asuitable gluing algorithm can be used to compute GW invariants in all genera ofany toric CY orbifold of dimension 3. We conjecture a correspondence with theDT orbifold vertex of Bryan-Cadman-Young.

Localization and Gluing of Orbifold Amplitudes: The Gromov-Witten Orbifold Vertex