Knot Floer homology detects fibred knots

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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 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.