The Last Three T-degrees in Triply-Graded Link Homology
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915295051907072 |
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| author | Li, Cailan |
| author_facet | Li, Cailan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Last Three T-degrees in Triply-Graded Link Homology Li, Cailan Representation Theory Geometric Topology Quantum Algebra 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. |
| title | The Last Three T-degrees in Triply-Graded Link Homology |
| topic | Representation Theory Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2505.14182 |