Abstract
Elements of the tropical vertex group are formal families of symplectomorphisms of the -dimensional algebraic torus. We prove that ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus zero relative Gromov-Witten 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 Gromov-Witten theory
Citation
Mark Gross. Rahul Pandharipande. Bernd Siebert. "The tropical vertex." Duke Math. J. 153 (2) 297 - 362, 1 June 2010. https://doi.org/10.1215/00127094-2010-025
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