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… (More)

Ozsváth and Szabó proved that knot Floer homology determines the genera of classical knots. We will generalize this deep result to the case of classical links, by adapting their method. Our proof… (More)

We observe that the main theorem in [4] immediately implies its analogue for closed 3–manifolds. Theorem 1. Suppose Y is a closed irreducible 3–manifold, F ⊂ Y is a closed connected surface of genus… (More)

We correct a mistake on the citation of JSJ theory in [4]. Some arguments in [4] are also slightly modified accordingly. An important step in [4] uses JSJ theory [2, 3] to deduce some topological… (More)

Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order… (More)

We define the action of the homology group H1(M,∂M) on the sutured Floer homology SFH(M,γ). It turns out that the contact invariant EH(M,γ, ξ) is usually sent to zero by this action. This fact allows… (More)

We study Dehn surgeries on null-homotopic knots that yield fibred 3-manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai’s theory of sutured… (More)

Suppose that X is a torus bundle over a closed surface with homologically essential fibers. LetXK be the manifold obtained by Fintushel–Stern knot surgery on a fiber using a knot K ⊂ S. We prove that… (More)

We prove that, for a link L in a rational homology 3–sphere, the link Floer homology detects the Thurston norm of its complement. This generalizes the previous results due to Ozsváth, Szabó and the… (More)

We show that if a surgery on a knot in a product sutured manifold yields the same product sutured manifold, then this knot is a 0or 1-crossing knot. The proof uses techniques from sutured manifold… (More)