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• W3005617476 abstract "This paper begins with a survey of some applications of Khovanov homology to low-dimensional topology, with an eye toward extending these results to $mathfrak{sl}(n)$ homologies. We extend Levine and Zemke's ribbon concordance obstruction from Khovanov homology to $mathfrak{sl}(n)$ homology for $n geq 2$, including the universal $mathfrak{sl}(2)$ and $mathfrak{sl}(3)$ homology theories. Inspired by Alishahi and Dowlin's bounds for the unknotting number coming from Khovanov homology and relying on spectral sequence arguments, we produce bounds on the alternation number of a knot. Lee and Bar-Natan spectral sequences also provide lower bounds on Turaev genus." @default.
• W3005617476 created "2020-02-24" @default.
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• W3005617476 date "2020-02-12" @default.
• W3005617476 modified "2023-09-23" @default.
• W3005617476 title "On Khovanov Homology and Related Invariants" @default.
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• W3005617476 doi "https://doi.org/10.48550/arxiv.2002.05247" @default.
• W3005617476 hasPublicationYear "2020" @default.
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