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Khovanov homology detects the trefoils

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arxiv 1801.07634 v2 pith:OI2TVPYU submitted 2018-01-23 math.GT math.SG

John A. Baldwin , Steven Sivek This is my paper · ORCID
classification math.GTmath.SG
keywords homologyinstantonkhovanovcontactdetectsfloerknotkronheimer
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abstract

We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer homology and contact geometry. It uses open books; the contact invariants we defined in the instanton Floer setting; a bypass exact triangle in sutured instanton homology, proven here; and Kronheimer and Mrowka's spectral sequence relating Khovanov homology with singular instanton knot homology. As a byproduct, we also strengthen a result of Kronheimer and Mrowka on $SU(2)$ representations of the knot group.

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  1. Fractional Dehn twist coefficients and rank bounds for categorified link invariants

    math.GT 2026-08 conditional novelty 7.0 of 10

    Fibered links whose monodromy twists many times around a boundary component have large next-to-top link Floer homology, and braid closures with large fractional Dehn twist coefficient have large annular Khovanov homology.

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