Link Floer homology detects the Thurston norm

By Yi Ni. 2006

75 citations recorded by the source corpus.

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 an ingredient of the proof, we show that knot Floer homology detects the genus of null-homologous links in rational homology spheres, which is a generalization of an earlier result of the author. Our argument uses the techniques due to Ozsvath and Szabo, Hedden and the author.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/00c5e03914b76a04d8626e5f9231f133249f475d

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Citations in the corpus

Floer simple manifolds and L-space intervals (2015, unknown): “More generally, it is known that ĤFK(K) determines both the Thurston norm of Y and whether it is fibred [35, 34, 26].”
On the geography and botany of knot Floer homology (2014, background): “For these, and all other detection theorems for Floer invariants known to the authors, the key facts have been that Floer homology detects the minimal genus of embedded surfaces in 3-manifolds representing a given homology class [61,74], and whether such surfaces arise as fibers in a fibration of th”
An algorithm for computing some Heegaard Floer homologies (2006, background): “onal topology. It gives an alternate proof of the Donaldson diagonalization theorem and the Thom conjecture for CP2 ([10]). Heegaard Floer homology also detects the Thurston norm of a three-manifold ([16, 7]). Moreover, knot Floer homology detects the genus ([13]) and ﬁberedness ([1, 6, 2]) of knots”
Contact surgeries and the transverse invariant in knot Floer homology (2008, background): “(4.3) Indeed, px0(B) = n1 (since x0 lies in the region between α1 and β1), while for all i > 0, pxi(B) = 0, since at each xi ∈ x′ which meets B, the four corners have local multiplicities 0, ni, 0 and −ni.”
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,…”
Topologically slice knots of smooth concordance order two (2012, background): “As described by Turaev [28], Spin–structures on a closed manifold correspond to equivalence classes of nonvanishing vector fields, where two are equivalent if homotopic off a ball.”
On Knot Floer Homology and Cabling: 2 (2008, methodology): “The existence of two independent Z filtrations allows one to define many auxilary knot invariants and in this paper we deal with a less robust invariant - the filtered chain homotopy type of the Z-filtration of ĈF (Y, s) obtained by setting one of the 1The depends on an identification of the…”