Inventiones mathematicae

, Volume 170, Issue 3, pp 577–608

Knot Floer homology detects fibred knots



Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in S3. We will prove this conjecture for null-homologous knots in arbitrary closed 3-manifolds. Namely, if K is a knot in a closed 3-manifold Y, Y-K is irreducible, and \(\widehat{HFK}(Y,K)\) is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsváth–Szabó, Ghiggini and the author. A corollary is that if a knot in S3 admits a lens space surgery, then the knot is fibred.


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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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