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An instanton take on some knot detection results

2024; American Mathematical Society; Linguagem: Inglês

10.1090/pspum/109/01991

2324-707X

John A. Baldwin, Steven Sivek,

Logic, programming, and type systems

We give new proofs that Khovanov homology detects the figure eight knot and the cinquefoils, and that HOMFLY homology detects 5 2 5_2 and each of the P ( − 3 , 3 , 2 n + 1 ) P(-3,3,2n+1) pretzel knots. For all but the figure eight these mostly follow the same lines as in previous work. The key difference is that in honor of Tom Mrowka’s 60th birthday, the arguments here use instanton Floer homology rather than knot Floer homology.