Related papers: Taut foliations in knot complements

Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint.…

This paper studies the existence of $2$-torsion in instanton Floer homology with $\mathbb{Z}$ coefficients for closed $3$-manifolds and singular knots. First, we show that the non-existence of $2$-torsion in the framed instanton Floer…

We prove an equivariant version of the Heegaard Floer link surgery formula. As a special case, this gives an equivariant knot surgery formula for equivariant knots in $S^3$. Our proof goes by way of a naturality theorem for certain bordered…

Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsvath-Szabo contact invariant we obtain an invariant of knots…

If a knot $K$ in $S^3$ admits a pair of truly cosmetic surgeries, we show that the surgery slopes are either $\pm 2$ or $\pm 1/q$ for some value of $q$ that is explicitly determined by the knot Floer homology of $K$. Moreover, in the former…

Motivated by the $L$-space conjecture, we prove left-orderability of certain Dehn fillings on integral homology solid tori with techniques first appearing in the work of Culler-Dunfield. First, we use the author's previous results to…

Using Taubes' periodic ends theorem, Auckly gave examples of toroidal and hyperbolic irreducible integer homology spheres which are not surgery on a knot in the three-sphere. We give an obstruction to a homology sphere being surgery on a…

We prove the nontriviality, at all integral levels n, of the filtration, F_n, of the classical topological knot concordance group recently defined by the authors and Kent Orr [COT]. Recall that this filtration is significant not only…

In the present paper we determine the Thurston-Bennequin invariant of graph divide links, which include all closed positive braids, all divide links and certain negative twist knots. As a corollary of this and a result of P. Lisca and A.I.…

We compute the knot Floer filtration induced by a cable of the meridian of a knot in the manifold obtained by large integer surgery along the knot. We give a formula in terms of the original knot Floer complex of the knot in the…

A taut foliation of a hyperbolic 3-manifold has the continuous extension property for leaves in almost every direction; that is, for each leaf of the universal cover of the foliation and almost every geodesic ray in the leaf, the limit of…

We study the sutured Floer homology invariants of the sutured manifold obtained by cutting a knot complement along a Seifert surface, R. We show that these invariants are finer than the "top term" of the knot Floer homology, which they…

We study finite type invariants of nullhomologous knots in a closed 3-manifold $M$ defined in terms of certain descending filtration $\{\mathscr{K}_n(M)\}_{n\geq 0}$ of the vector space $\mathscr{K}(M)$ spanned by isotopy classes of…

We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere. Specifically, if surgery along a knot produces a lens space, then there exists an equivalent surgery along a Berge knot with the same knot…

We consider homologically essential simple closed curves on Seifert surfaces of genus one knots in $S^3$, and in particular those that are unknotted or slice in $S^3$. We completely characterize all such curves for most twist knots: they…

We provide a way to produce knots in $S^3$ from signed chord diagrams, and prove that every knot can be produced in this way. Using these diagrams, we generalize the fundamental theorem of finite type invariants. We also provide moves for…

We construct cobordism maps for the \textit{minus} version of instanton knot homology associated to a \textit{specially decorated} knot cobordisms of arbitrary genus between two null-homologous knots in closed oriented $3$-manifolds. As an…

We prove that if positive integer p-surgery along a knot K \subset S^3 produces an L-space and it bounds a sharp 4-manifold, then the knot genus obeys the bound 2g(K) -1 \leq p - \sqrt{3p+1}. Moreover, there exists an infinite family of…

Suppose $K \subset S^3$ is a knot and suppose $p$ and $q$ are co-prime integers with $q\ge 1$. For any field $\mathbb{K}$, we establish a dimension formula for the framed instanton homology of knot surgeries: $$ \dim I^\sharp(S^3_{p/q}(K);…

Let K be a knot in S^3, and M and M' be distinct Dehn surgeries along K. We investigate when M covers M'. When K is a torus knot, we provide a complete classification of such covers. When K is a hyperbolic knot, we provide partial results…