All Outputs (2)

Cosmetic operations and Khovanov multicurves (2023)
Journal Article
Kotelskiy, A., Lidman, T., Moore, A. H., Watson, L., & Zibrowius, C. (2024). Cosmetic operations and Khovanov multicurves. Mathematische Annalen, 389(3), 2903-2930. https://doi.org/10.1007/s00208-023-02697-5

We prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invariants Kh~ and BN~. We apply the same techniques to reprove a result of... Read More about Cosmetic operations and Khovanov multicurves.

A mnemonic for the Lipshitz–Ozsváth–Thurstoncorrespondence (2023)
Journal Article
Kotelskiy, A., Watson, L., & Zibrowius, C. (2023). A mnemonic for the Lipshitz–Ozsváth–Thurstoncorrespondence. Algebraic & geometric topology, 23(6), 2519-2543. https://doi.org/10.2140/agt.2023.23.2519

When k is a field, type D structures over the algebra k[u,v]∕(uv) are equivalent to immersed curves decorated with local systems in the twice-punctured disk. Consequently, knot Floer homology, as a type D structure over k[u,v]∕(uv), can be viewed as... Read More about A mnemonic for the Lipshitz–Ozsváth–Thurstoncorrespondence.