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Skein valued curve counts, basic holomorphic disks, and HOMFLY homology Ekholm, Tobias


We describe invariant counts of holomorphic curves in a Calabi-Yau 3-fold with boundary in a Lagrangian in the skein module of that Lagrangian. We show how to turn this into concrete counts for the toric brane in the resolved conifold. This leads to a notion of basic holomorphic disks for any knot conormal in the resolved conifold. These basic holomorphic disks seem to generate HOMFLY homology in the basic representation. We give a conjectural description of similar holomorphic object generating parts of higher symmetric representation HOMFLY homology and verify some predictions coming from this conjecture in examples.

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