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The
cosmetic crossing conjecture for split links
Joshua Wang |
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Geometry & Topology 26 (2022) 2941–3053
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Abstract |
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Given a band sum of a split two-component link along a nontrivial band, we obtain a family of knots indexed by the integers by adding any number of full twists to the band. We show that the knots in this family have the same Heegaard knot Floer homology and the same instanton knot Floer homology. In contrast, a generalization of the cosmetic crossing conjecture predicts that the knots in this family are all distinct. We verify this prediction by showing that any two knots in this family have distinct Khovanov homology. Along the way, we prove that each of the three knot homologies detects the trivial band. |
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Keywords
cosmetic, crossing, nugatory, Khovanov, Floer, instanton,
Heegaard Floer, knot Floer, band sum, split links,
detection
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Mathematical Subject Classification
Primary: 57K10, 57K18
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References |
Publication
Received: 24 July 2020
Revised: 2 July 2021
Accepted: 10 August 2021
Published: 23 January 2023
Proposed: Ciprian Manolescu
Seconded: Paul Seidel, Tomasz Mrowka
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Authors |
| Joshua Wang | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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