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arXiv · 2505.14182

The Last Three T-degrees in Triply-Graded Link Homology

Cailan Li
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Abstract

We investigate the structure of reduced triply graded link homology $\overline{\mathrm{HHH}}$ 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 $\overline{\mathrm{HHH}}$ 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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Cailan Li. 2025-05-20. The Last Three T-degrees in Triply-Graded Link Homology. https://arxiv.org/abs/2505.14182

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