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Khovanov homology and exotic surfaces in the 4-ball

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arxiv 2108.04810 v2 pith:WOLEQHC3 submitted 2021-08-10 math.GT

Kyle Hayden , Isaac Sundberg This is my paper · ORCID
classification math.GT
keywords homologykhovanovmapsambientballcobordismsurfacesascending
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We show that the cobordism maps on Khovanov homology can distinguish smooth surfaces in the 4-ball that are exotically knotted (i.e., isotopic through ambient homeomorphisms but not ambient diffeomorphisms). We develop new techniques for distinguishing cobordism maps on Khovanov homology, drawing on knot symmetries and braid factorizations. We also show that Plamenevskaya's transverse invariant in Khovanov homology is preserved by maps induced by positive ascending cobordisms.

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  1. Notes on Khovanov homology

    math.GT 2025-01 conditional

    Expository lecture notes surveying Khovanov homology, its applications, and related invariants, with no new mathematical results.

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