For any braid, the outermost three T-degree layers of reduced triply-graded HOMFLY homology are determined explicitly, and are almost entirely zero with only a few one-dimensional k-modules.
The two-color Soergel calculus
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The Last Three T-degrees in Triply-Graded Link Homology
For any braid, the outermost three T-degree layers of reduced triply-graded HOMFLY homology are determined explicitly, and are almost entirely zero with only a few one-dimensional k-modules.