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