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A mathematical theory of the topological vertex
"... Abstract. We have developed a mathematical theory of the topological vertex— a theory that was originally proposed by M. Aganagic, A. Klemm, M. Mariño, and C. Vafa on effectively computing GromovWitten invariants of smooth toric CalabiYau threefolds derived from duality between open string theory ..."
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Cited by 15 (7 self)
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Abstract. We have developed a mathematical theory of the topological vertex— a theory that was originally proposed by M. Aganagic, A. Klemm, M. Mariño, and C. Vafa on effectively computing GromovWitten invariants of smooth toric CalabiYau threefolds derived from duality between open string theory of smooth CalabiYau threefolds and ChernSimons theory on three manifolds. 1.
The tropical vertex
"... Abstract. Elements of the tropical vertex group are formal families of symplectomorphisms of the 2dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus 0 relative GromovWitten invariants of toric surfaces. ..."
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Cited by 6 (3 self)
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Abstract. Elements of the tropical vertex group are formal families of symplectomorphisms of the 2dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus 0 relative GromovWitten invariants of toric surfaces. The relative invariants which arise have full tangency to a toric divisor at a single unspecified point. The method uses scattering diagrams, tropical curve counts, degeneration formulas, and exact multiple cover calculations in orbifold GromovWitten theory. Contents