Knot Floer homology detects fibred knots

Details Knot Floer homology detects fibred knots Knot Floer homology detects fibred knots

2006-07-06

arxiv.org/abs/math/0607156v4

Mathematics

Geometric Topology

version 4: incorporates referee's suggestions, to appear in Inventiones Mathematicae

Scientific paper

10.1007/s00222-007-0075-9

Ozsv\'ath and Szab\'o 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 $\hat{HFK}(Y,K)$ is monic, then $K$ is fibred. The proof relies on previous works due to Gabai, Ozsv\'ath--Szab\'o, 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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