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Abstract We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering.In particular, this leads to a purely knot Floer-theoretic characterization of tight contact structures, by the work of Honda–Kazez–Matić.Our proof makes use of the relationship between the Heegaard Floer homology of mapping tori and the symplectic Floer homology of area-preserving surface diffeomorphisms.We describe applications of this work to Dehn surgeries and taut foliations.
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We say a null-homologous knot in a -manifold has Property G, if the Thurston norm and fiberedness of the complement of is preserved under the zero surgery on . In this paper, we will show that, if the smooth -genus of (in a certain homology class) in , where is a rational homology sphere, is smaller than the Seifert genus of , then has Property G. When the smooth -genus is , can be taken to be any closed, oriented -manifold.more » « less
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Abstract We prove that if K is a nontrivial null-homotopic knot in a closed oriented 3–manfiold Y such that $Y-K$ does not have an $$S^1\times S^2$$ summand, then the zero surgery on K does not have an $$S^1\times S^2$$ summand. This generalises a result of Hom and Lidman, who proved the case when Y is an irreducible rational homology sphere.more » « less
