Knot Floer homology detects fibred knots

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.

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

References in corpus (7)

• Floer homology and knot complements
• Holomorphic disks and genus bounds
• Holomorphic discs and sutured manifolds
• Heegaard Floer homologies and contact structures
• Sutured Heegaard diagrams for knots
• Knot Floer homology in cyclic branched covers
• Knot Floer homology detects genus-one fibred knots

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