Knot Floer homology detects fibred knots

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 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