Related papers: Links with surgery yielding the 3-sphere

A well-known conjecture in knot theory says that the percentage of hyperbolic knots amongst all of the prime knots of $n$ or fewer crossings approaches $100$ as $n$ approaches infinity. In this paper, it is proved that this conjecture…

We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions.…

We show the existence of infinitely many knot exteriors where each of which contains meridional essential surfaces of any genus and (even) number of boundary components. That is, the compact surfaces that have a meridional essential…

Given a cusped hyperbolic 3-manifold with finite volume, we define two types of complex parameters which capture geometric information about the preimages of geodesic arcs traveling between cusp cross-sections. We prove that these…

This chapter from the upcoming Handbook of Knot Theory (eds. Menasco and Thistlethwaite) shows how to construct hyperbolic structures on link complements and perform hyperbolic Dehn filling. Along with a new elementary exposition of the…

By work of W. Thurston, knots and links in the 3-sphere are known to either be torus links, or to contain an essential torus in their complement, or to be hyperbolic, in which case a unique hyperbolic volume can be calculated for their…

For any hyperbolic genus one 2-bridge knot in the 3-sphere, we show that the resulting manifold by $r$-surgery on the knot has left-orderable fundamental group if the slope $r$ lies in some range which depends on the knot.

Przytycki and Sokolov proved that a three-manifold admits a semi-free action of the finite cyclic group of order $p$ with a circle as the set of fixed points if and only if $M$ is obtained from the three-sphere by surgery along a strongly…

We give examples of knots in a genus 2 handlebody which have nontrivial Dehn surgeries yielding handlebodies and show that these knots are not 1--bridge.

The work of J{\o}rgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. In this paper, we construct examples showing that the number of hyperbolic knot complements with a…

We demonstrate the existence of minimal simplicial $n$-complexes which inevitably contain a nonsplittable two-component link formed by an $(n-1)$-sphere and an $n$-sphere in any embedding into $\mathbb{R}^{2n}$. This provides a…

Let $M_{\lambda}$ be the $\lambda$-component Milnor link. For $\lambda \ge 3$, we determine completely when a finite slope surgery along $M_{\lambda}$ yields a lens space including $S^3$ and $S^1\times S^2$, where {\it finite slope surgery}…

We prove that there are infinitely many non-homeomorphic hyperbolic knot complements $S^3\setminus K_i = \mathbb{H}^3/\Gamma_i$ for which $\Gamma_i$ contains elements whose trace is an algebraic non-integer.

We construct an algorithm that lists all closed essential surfaces in the complement of a knot that lies on the fiber of a trefoil or figure eight knot. Such knots are Berge knots and hence admit lens space surgeries. Furthermore they may…

Let $F$ be a compact orientable surface with nonempty boundary other than a disk. Let $L$ be a link in $F \times I$ with a connected weakly prime cellular alternating projection to $F$. We provide simple conditions that determine exactly…

The work of Jorgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. We show that there is an infinite sequence of closed orientable hyperbolic 3-manifolds, obtained by…

Let $M$ be a $3$--dimensional handlebody of genus $g$. This paper gives examples of hyperbolic knots in $M$ with arbitrarily large genus $g$ bridge number which admit Dehn surgeries which are boundary-reducible manifolds.

In this paper we find the first infinite family of hyperbolic 3-manifolds which admit tight contact structures but do not have any tight projectively Anosov flow. These manifolds are obtained as rational surgeries on the figure eight knot.

Let K be a knot in the 3-sphere. A slope p/q is said to be characterising for K if whenever p/q surgery on K is homeomorphic, via an orientation-preserving homeomorphism, to p/q surgery on another knot K' in the 3-sphere, then K and K' are…

We study the symplectic geometry of the moduli space of closed n-gons with fixed side-lengths in hyperbolic 3-space. We prove that these moduli spaces have a symplectic structure coming from Poisson Lie theory. We construct completely…