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, proved 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 representations of the knot group.
Citation
John A. Baldwin. Steven Sivek. "Khovanov homology detects the trefoils." Duke Math. J. 171 (4) 885 - 956, 15 March 2022. https://doi.org/10.1215/00127094-2021-0034
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