Knot Floer homology detects genus-one fibred knots

Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on contact topology and Gabai's theory of sutured manifold decomposition. We implement this strategy for genus-one knots, obtaining as a corollary that if rational surgery on a knot K gives the Poincar\'e homology sphere Σ(2,3,5), then K is the left-handed trefoil knot.