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Knot Floer homology detects fibred knots
  • Yi Ni
  • Mathematics
  • 20 September 2007
Ozsvath and Szabo 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 inExpand
Cosmetic surgeries on knots in $S^3$
Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in $S^3$,Expand
Knot Floer homology detects fibred knots
  • Yi Ni
  • Mathematics
  • 6 July 2006
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 aExpand
Link Floer homology detects the Thurston norm
  • Yi Ni
  • Mathematics
  • 16 April 2006
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 result has been proved by Ozsvath and Szabo for links in S^3. AsExpand
Heegaard Floer homology and fibred 3-manifolds
  • Yi Ni
  • Mathematics
  • 14 June 2007
<abstract abstract-type="TeX"><p>Given a closed $3$-manifold $Y$, we show that the Heegaard Floer homology determines whether $Y$ fibres over the circle with a fibre of negative Euler characteristic.Expand
Detection of knots and a cabling formula for A-polynomials
We say that a given knot $J\subset S^3$ is detected by its knot Floer homology and $A$-polynomial if whenever a knot $K\subset S^3$ has the same knot Floer homology and the same $A$-polynomial asExpand
Characterizing slopes for torus knots
A slope p/q is called a characterizing slope for a given knot K_0 in S^3 if whenever the p/q–surgery on a knot K in S^3 is homeomorphic to the p/q–surgery on K_0 via an orientation preservingExpand
Homological actions on sutured Floer homology
  • Yi Ni
  • Mathematics
  • 14 October 2010
We define the action of the homology group H_1(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 allowsExpand
Homological actions on sutured Floer homology
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 allowsExpand
Nonseparating spheres and twisted Heegaard Floer homology
  • Yi Ni
  • Mathematics
  • 23 February 2009
If a 3–manifold Y contains a nonseparating sphere, then some twisted Heegaard Floer homology of Y is zero. This simple fact allows us to prove several results about Dehn surgery on knots in suchExpand
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