David Popović

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math.GT2026

Khovanov-Rozansky homology over $F [U, V]$

David Popović

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…

math.GT2026

Reduced Khovanov-Rozansky homology

David Popović

We introduce a variant of reduced Khovanov-Rozansky homology defined in terms of the variables alpha_1, ..., alpha_{n-1} that correspond to the regions between the strands. We rigo…

math.GT2024

Knots of low knot Floer width

David Popović

This paper classifies the chain homotopy equivalence types of knot Floer complexes $C F K_{F [U, V]} (K)$ of knot Floer width 2. They have no nontrivial local systems. As an ap…

Khovanov-Rozansky homology over F[U,V]

Reduced Khovanov-Rozansky homology

Knots of low knot Floer width

Khovanov-Rozansky homology over $F [U, V]$