Knot Floer homology detects fibred knots

By Yi Ni. 2006

142 citations recorded by the source corpus.

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 closed 3-manifold Y, Y-K is irreducible, and $\widehat{HFK}(Y,K)$ is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsváth–Szabó, Ghiggini and the author. A corollary is that if a knot in S3 admits a lens space surgery, then the knot is fibred.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/a9113cd953bc2488ec73341faed2bbc267ec2084

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Citations in the corpus

Knots, sutures, and excision (2008, unknown): “We now consider a maximal product pair i : [−1, 1] × E →֒ (M,γ) as in [23, 24] and the induced map i∗ : H1([−1, 1] × E) → H1(M).”
On the Khovanov and knot Floer homologies of quasi-alternating links (2007, unknown): “G T ] 2 6 M ar 2 00”
Lens space surgeries and L-space homology spheres (2007, unknown): “G T ] 12 O ct 2”
Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology (2007, methodology): “…homology in manifolds other than S3 has been shown to detect the Thurston norm of a link complement [OS06a],[Ni06a], whether a knot is fibered [Ni06b] and has had applications to questions related to the concordance classes of knots in S3 through the double-branched covering operation [MO05,…”
Knot Floer homology detects fibred knots (2007, methodology): “We are extremely grateful to Peter Kronheimer for pointing out the mistake in [4].”