Structures in HOMFLY-PT homology

Alex Chandler; Eugene Gorsky

doi:10.1080/10586458.2023.2300412

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arXiv · 2209.13058

Structures in HOMFLY-PT homology

Alex Chandler·Eugene Gorsky

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Abstract

We study the structure of triply graded Khovanov-Rozansky homology using both the data recently computed by Nakagane and Sano for knots up to 11 crossings, and the $\mathfrak{sl}(2)$ action defined by the second author, Hogancamp and Mellit. In particular, we compute the HOMFLY-PT $S$-invariant for all knots in the dataset, and compare it to the $\mathfrak{sl}(N)$ concordance invariants.

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BibTeX RIS

Alex Chandler, Eugene Gorsky. 2022-09-26. Structures in HOMFLY-PT homology. https://doi.org/10.1080/10586458.2023.2300412

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