Do Heegaard Floer homology detect fibred knot in general oriented 3-manifolds other than $S^3$? If the answer is yes could you give a reference.



Do Heegaard Floer homology detect fibred knot in general oriented 3-manifold?
This is known for any knot in a closed, oriented 3-manifold whose complement is irreducible. Ni proved this in [Knot Floer homology detects fibred knots](http://arxiv.org/abs/math/0607156), building on [Ghiggini](http://arxiv.org/abs/math/0603445)'s proof in the genus 1 case; another proof was given by [Juhász](http://arxiv.org/abs/math/0609779) (see theorem 9.11).


