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arXiv · 2412.15454

The skein valued mirror of the topological vertex

Tobias Ekholm·Pietro Longhi·Vivek Shende
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Abstract

We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Using 1-parameter families of curves at infinity, we derive three skein valued operator equations which must annihilate the count, and which dequantize to a mirror of the geometry. We show algebraically that the resulting equations determine the count uniquely, and that the result agrees with the topological vertex from topological string theory.

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Tobias Ekholm, Pietro Longhi, Vivek Shende. 2024-12-19. The skein valued mirror of the topological vertex. https://arxiv.org/abs/2412.15454

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