Year: 2025
Type: dissertation
Abstract: The package of Type A link homology theories is controlled by (Type A) singular Soergel bimodules. Weintroduce several families of “Fray” functors on singular Soergel bimodules, modeled on constructions incategorical representation theory. We prove that each of these families gives rise to a corresponding familyof column-colored link homologies interpolating between existing constructions of column-colored homology.Finally, we use Fray functors to compute the column-colored HOMFLY homology of positive torus knots,resulting in the first verification of mirror symmetry conjectures for colored HOMFLY homology in nontrivialcolors.
DOI: 10.17615/h5mb-e586
Author: Conners, Luke Gregory
Institution: University of North Carolina at Chapel Hill
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6925620694
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