Khovanov homology detects the trefoils

John A. Baldwin; Steven Sivek

doi:10.1215/00127094-2021-0034

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arXiv · 1801.07634

Khovanov homology detects the trefoils

John A. Baldwin·Steven Sivek

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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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John A. Baldwin, Steven Sivek. 2018-01-23. Khovanov homology detects the trefoils. https://doi.org/10.1215/00127094-2021-0034

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