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Knot Floer homology detects fibred knots

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An Erratum to this article was published on 13 February 2009

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.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, New Jersey, 08544, USA

    Yi Ni

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  1. Yi Ni
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Correspondence to Yi Ni.

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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.

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Ni, Y. Knot Floer homology detects fibred knots. Invent. math. 170, 577–608 (2007). https://doi.org/10.1007/s00222-007-0075-9

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  • DOI: https://doi.org/10.1007/s00222-007-0075-9

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