, Volume 170, Issue 3, pp 577-608
Date: 20 Sep 2007

Knot Floer homology detects fibred knots

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Abstract

Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in S 3. 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 S 3 admits a lens space surgery, then the knot is fibred.

Dedicated to Professor Boju Jiang on the occasion of his 70th birthday

Mathematics Subject Classification (2000)

57R58, 57M27, 57R30
An erratum to this article can be found online at http://dx.doi.org/10.1007/s00222-009-0174-x.