Khovanov homology detects the trefoils
نویسندگان
چکیده
We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer and contact geometry. It uses open books; invariants we defined instanton setting; a bypass exact triangle sutured homology, proven here; Kronheimer Mrowka's spectral sequence relating with singular knot homology. As byproduct, also strengthen result Mrowka on $SU(2)$ representations group.
منابع مشابه
Khovanov Homology Detects the Trefoils
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 homolo...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2022
ISSN: ['1547-7398', '0012-7094']
DOI: https://doi.org/10.1215/00127094-2021-0034