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arXiv · 0902.0779

The tropical vertex

Mark Gross·Rahul Pandharipande·Bernd Siebert
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Abstract

Elements of the tropical vertex group, introduced by Kontsevich and Soibelman, are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus 0 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.

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Mark Gross, Rahul Pandharipande, Bernd Siebert. 2009-02-04. The tropical vertex. https://doi.org/10.1215/00127094-2010-025

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