15 March 2022 Khovanov homology detects the trefoils
John A. Baldwin, Steven Sivek
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Duke Math. J. 171(4): 885-956 (15 March 2022). DOI: 10.1215/00127094-2021-0034

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 SU(2) representations of the knot group.

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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

Information

Received: 10 January 2018; Revised: 27 October 2020; Published: 15 March 2022
First available in Project Euclid: 14 March 2022

MathSciNet: MR4393789
zbMATH: 1494.57020
Digital Object Identifier: 10.1215/00127094-2021-0034

Subjects:
Primary: 57M27
Secondary: 57R17 , 57R58

Keywords: contact geometry , instanton Floer homology , Khovanov homology , trefoil

Rights: Copyright © 2022 Duke University Press

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Vol.171 • No. 4 • 15 March 2022
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