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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 in… Expand

Cosmetic surgeries on knots in $S^3$

- Yi Ni, Zhongtao Wu
- Mathematics
- 23 September 2010

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 a… Expand

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. As… Expand

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 as… Expand

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 preserving… Expand

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 allows… Expand

Homological actions on sutured Floer homology

- Yi Ni
- 2014

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… Expand

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 such… Expand

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