The Last Three T-degrees in Triply-Graded Link Homology
Abstract
We investigate the structure of reduced triply graded link homology HHH in the top/bottom three T-degrees for links arising as closures of positive/negative braids. Using a diagrammatic approach to the Hochschild cohomology of Soergel bimodules, we provide explicit computations of HHH as R-modules in these degrees. Our results reveal that the homology here is often zero, especially in the negative braid case, and display striking uniformity.
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