Related papers: Persistently laminar tangles

In the first part of this paper, we construct infinitely many hyperbolic closed 3-manifolds which admit no symplectic fillable contact structure. All these 3-manifolds are obtained by Dehn surgeries along L-space knots or L-space…

Attaching a 2-handle to a genus two or greater boundary component of a 3-manifold is a natural generalization of Dehn filling a torus boundary component. We prove that there is an interesting relationship between an essential surface in a…

We prove that there is a knot $K$ transverse to $\xi_{std}$, the tight contact structure of $S^3$, such that every contact 3-manifold $(M, \xi)$ can be obtained as a contact covering branched along $K$. By contact covering we mean a map…

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture says that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. Here, we discuss two interrelated…

We survey aspects of classical combinatorial sutured manifold theory and show how they can be adapted to study exceptional Dehn fillings and 2-handle additions. As a consequence we show that if a hyperbolic knot $\beta$ in a compact,…

The cosmetic crossing conjecture (also known as the "nugatory crossing conjecture") asserts that the only crossing changes that preserve the oriented isotopy class of a knot in the 3-sphere are nugatory. We use the Dehn surgery…

Let $K= K(w,b,t)$ be a 1-bridge braid in a solid torus $V$, and let $\gamma$ be a $(p,q)$ curve on the torus $T = \partial V$ of the exterior $M_K$ of $K$. It will be shown that Dehn filling on $T$ along $\gamma$ produces a solid torus if…

For a knot $K$ in a homology $3$-sphere $\Sigma$, let $M$ be the result of $2/q$-surgery on $K$, and let $X$ be the universal abelian covering of $M$. Our first theorem is that if the first homology of $X$ is finite cyclic and $M$ is a…

We give an alternative proof of a recent theorem of Tange using the technology of changemaker lattices. Specifically, for $K\subset S^3$ a non-trivial knot with a lens space surgery, we give constraints on the Alexander polynomial of $K$…

Band surgery is an operation relating pairs of knots or links in the three-sphere. We prove that if two quasi-alternating knots $K$ and $K'$ of the same square-free determinant are related by a band surgery, then the absolute value of the…

We study an invariant of a 3-manifold which consists of Reidemeister torsion for linear representations which pass through a finite group. We show a Dehn surgery formula on this invariant and compute that of a Seifert manifold over $S^2$.…

Consider a continuous flow in $\mathbb{R}^3$ or any orientable $3$-manifold. Let $(Q_1, Q_0)$ be an index pair in the sense of Conley and consider the region $N := \overline{Q_1 - Q_0}$. (An example of this is a compact $3$-manifold $N$…

We study knots in $S^3$ with infinitely many $SU(2)$-cyclic surgeries, which are Dehn surgeries such that every representation of the resulting fundamental group into $SU(2)$ has cyclic image. We show that for every such nontrivial knot…

A group theoretic version of Dehn surgery is studied. Starting with an arbitrary relatively hyperbolic group $G$ we define a peripheral filling procedure, which produces quotients of $G$ by imitating the effect of the Dehn filling of a…

We describe four hyperbolic knot complements in $\mathbb{S}^3$, each of which covers a prism orbifold: the quotient of $\mathbb{H}^3$ by the action of a discrete group generated by reflections in the faces of a polyhedron that has the…

In this short note, we prove that every closed, oriented, connected 3-manifold arises as Dehn surgery along a braid positive link.

New obstructions for embedding one compact oriented 3-manifold in another are given. A theorem of D. Krebes concerning 4-tangles embedded in links arises as a special case. Algebraic and skein-theoretic generalizations for 2n-tangles…

To a hyperbolic manifold one can associate a canonical projective structure and ask whether it can be deformed or not. In a cusped manifold, one can ask about the existence of deformations that are trivial on the boundary. We prove that if…

Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371…

Suppose F is a compact orientable surface, K is a knot in F x I, and N is the 3-manifold obtained by some non-trivial surgery on K. If F x {0} compresses in N, then there is an annulus in F x I with one end K and the other end an essential…