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arXiv · 2405.00875

Fray functors and equivalence of colored HOMFLYPT homologies

Luke Conners
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Abstract

We construct several families of functors on the homotopy category of singular Soergel bimodules that mimic cabling and insertion of column-colored projectors. We use these functors to identify the intrinsically-colored homology of Webster--Williamson and the projector-colored homology of Elias--Hogancamp for an arbitrary link, up to multiplication by a polynomial in the quantum degree $q$. Combined with the results of arXiv:2303.16271, this establishes parity results for the intrinsic column-colored homology of positive torus knots, partially resolving a conjecture of Hogancamp--Rose--Wedrich in arXiv:2107.09590.

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Luke Conners. 2024-05-01. Fray functors and equivalence of colored HOMFLYPT homologies. https://arxiv.org/abs/2405.00875

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