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An action of the Witt algebra on Khovanov-Rozansky homology
[Submitted on 31 Jan 2025 (v1), last revised 2 Jun 2026 (this ve · 2026-06-03 · via math updates on arXiv.org

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Abstract:We construct an action of the positive part of the Witt algebra on Khovanov--Rozansky $\mathfrak{gl}_N$-link homology and show that link cobordisms induce equivariant maps between twists of the homology. Moreover, the state spaces of simple webs are identified with standard representations of the Witt algebra on polynomials. Some simple relations to Lee homology and genus bounds are derived from the analysis of this presentation.

Submission history

From: Felix Roz [view email]
[v1] Fri, 31 Jan 2025 12:41:52 UTC (68 KB)
[v2] Thu, 27 Mar 2025 11:34:55 UTC (70 KB)
[v3] Tue, 2 Jun 2026 17:35:53 UTC (76 KB)