Geodesic
Floer homology and non-fibered knot detection
Forum of Mathematics, Pi, Tome 13 (2025) no. 1, p. e1

Voir la notice de l'article provenant de la source Cambridge University Press

We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots and that HOMFLY homology detects infinitely many knots; these theories were previously known to detect a mere six knots, all fibered. These results rely on our main technical theorem, which gives a complete classification of genus-1 knots in the 3-sphere whose knot Floer homology in the top Alexander grading is 2-dimensional. We discuss applications of this classification to problems in Dehn surgery which are carried out in two sequels. These include a proof that $0$-surgery characterizes infinitely many knots, generalizing results of Gabai from his 1987 resolution of the Property R Conjecture. 
Baldwin, John A.; Sivek, Steven. Floer homology and non-fibered knot detection. Forum of Mathematics, Pi, Tome 13 (2025) no. 1, p. e1. doi: 10.1017/fmp.2024.28
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