A mathematical theory of the topological vertex

We have developed a mathematical theory of the topological vertex-a theory that was originally proposed by M Aganagic, A Klemm, M Marino and C Vafa on effectively computing Gromov-Witten invariants of smooth toric Calabi-Yau threefolds derived from duality between open string theory of smooth Calabi-Yau threefolds and Chern-Simons theory on three-manifolds.