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Colored HOMFLYPT counts holomorphic curves

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arxiv 2101.00619 v1 pith:Y7RJM5LJ submitted 2021-01-03 math.SG hep-thmath.GT

Tobias Ekholm , Vivek Shende This is my paper · ORCID
classification math.SGhep-thmath.GT
keywords holomorphiccurvescoloredcounthomflyptlinkresultagrees
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We compute the contribution of all multiple covers of an isolated rigid embedded holomorphic annulus, stretching between Lagrangians, to the skein-valued count of open holomorphic curves in a Calabi-Yau 3-fold. The result agrees with the predictions from topological string theory and we use it to prove the Ooguri-Vafa formula that identifies the colored HOMFLYPT invariants of a link with a count of holomorphic curves ending on the conormal Lagrangian of the link in the resolved conifold. This generalizes our previous work which proved the result for the fundamental color.

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  1. The skein valued mirror of the topological vertex

    math.SG 2024-12 conditional novelty 8.0 of 10

    Holomorphic curve counts in C3 with toric Lagrangian boundary obey skein operator equations whose unique solution is the topological vertex.

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