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arXiv · 2608.29986

Khovanov-Rozansky homology over $\mathbb{F}[U,V]$

David Popović
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Abstract

We define a 'full' version of Khovanov-Rozansky homology: a chain complex CH(K) over F[U,V] whose chain homotopy type is a knot invariant and which has the property that setting U = V = 0 recovers the reduced Khovanov-Rozansky homology. We explore the algebraic structure of CH(K) and show that a variation of the structure theorem for knot Floer homology applies. This allows us to define counterparts to knot Floer concordance invariants $\tau$, $\epsilon$ and $\phi_j$ in the Khovanov-Rozansky setting.

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David Popović. 2026-08-30. Khovanov-Rozansky homology over $\mathbb{F}[U,V]$. https://arxiv.org/abs/2608.29986

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