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      Floer Simple Manifolds and L-Space Intervals

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          Abstract

          An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-space filling, or an interval of L-space fillings. In the latter case, which we call "Floer simple," we construct an invariant which computes the interval of L-space filling slopes from the Turaev torsion and a given slope from the interval's interior. As applications, we give a new proof of the classification of Seifert fibered L-spaces over \(S^2\), and prove a special case of a conjecture of Boyer and Clay about L-spaces formed by gluing three-manifolds along a torus.

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          On knot Floer homology and lens space surgeries

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            Foliations and the topology of 3-manifolds

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              Knot Floer homology detects fibred knots

              Yi Ni (2006)
              Ozsv\'ath and Szab\'o 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 a closed 3--manifold \(Y\), \(Y-K\) is irreducible, and \(\hat{HFK}(Y,K)\) is monic, then \(K\) is fibred. The proof relies on previous works due to Gabai, Ozsv\'ath--Szab\'o, Ghiggini and the author. A corollary is that if a knot in \(S^3\) admits a lens space surgery, then the knot is fibred.
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                Author and article information

                Journal
                2015-08-24
                2015-11-24
                Article
                1508.05900
                ec437446-5817-4245-9a7c-5a2b3c500007

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                57M27
                50 pages, 2 figures
                math.GT

                Geometry & Topology
                Geometry & Topology

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