Related papers: Surgical distance between lens spaces

We show that there exist infinitely many pairs of distinct knots in the 3-sphere such that each pair can yield homeomorphic lens spaces by the same Dehn surgery. Moreover, each knot of the pair can be chosen to be a torus knot, a satellite…

Baker showed that 10 of the 12 classes of Berge knots are obtained by surgery on the minimally twisted 5-chain link. In this article we enumerate all hyperbolic knots in S^3 obtained by surgery on the minimally twisted 5 chain link that…

For a hyperbolic knot in the 3-sphere, at most finitely many Dehn surgeries yield non-hyperbolic 3-manifolds. As a typical case of such an exceptional surgery, a toroidal surgery is one that yields a closed 3-manifold containing an…

We show that on a hyperbolic knot $K$ in $S^3$, the distance between any two finite surgery slopes is at most two and consequently there are at most three nontrivial finite surgeries. Moreover in case that $K$ admits three nontrivial finite…

This paper concerns the Dehn surgery construction, especially those Dehn surgeries leaving the manifold unchanged. In particular, we describe an oriented 1-cusped hyperbolic 3-manifold X with a pair of slopes r_1, r_2 such that the Dehn…

It is conjectured that a hyperbolic knot admits at most three Dehn surgeries which yield closed three manifolds containing incompressible tori. We show that there exist infinitely many hyperbolic knots which attain the conjectural maximum…

We classify all the non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic Dehn fillings of…

We show that, for any given 3-manifold M, there are at most finitely many hyperbolic knots K in the 3-sphere and fractions p/q (with q > 22), such that M is obtained by p/q surgery along K. This is a corollary of the following result. If M…

For any n\ge 2, we give infinitely many unsplittable links of n components in the 3-sphere which admit non-trivial surgery yielding the 3-sphere again and whose components are mutually distinct hyperbolic knots. Berge and Kawauchi gave…

If a closed, orientable hyperbolic 3--manifold M has volume at most 1.22 then H_1(M;Z_p) has dimension at most 2 for every prime p not 2 or 7, and H_1(M;Z_2) and H_1(M;Z_7) have dimension at most 3. The proof combines several deep results…

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…

In this article, we define the contact surgery distance of two contact 3-manifolds $(M,\xi)$ and $(M',\xi')$ as the minimal number of contact surgeries needed to obtain $(M,\xi)$ from $(M',\xi')$. Our main result states that the contact…

The main theorem of this paper is a generalisation of well known results about Dehn surgery to the case of attaching handlebodies to a simple 3-manifold. The existence of a finite set of `exceptional' curves on the boundary of the…

Let $K$ be a hyperbolic knot in the 3-sphere. If $r$-surgery on $K$ yields a lens space, then we show that the order of the fundamental group of the lens space is at most $12g-7$, where $g$ is the genus of $K$. If we specialize to genus one…

This paper describes a Dehn surgery approach to generating asymmetric hyperbolic manifolds with two distinct lens space fillings. Such manifolds were first identified in work of Dunfield-Hoffman-Licata as the result of a computer search of…

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,…

We show that the distance of a link $K$ with respect to a bridge surface of any genus determines a lower bound on the genus of essential surfaces and Heegaard surfaces in the manifolds that result from non-trivial Dehn surgeries on the…

We determine all hyperbolic 3-manifolds $M$ admitting two toroidal Dehn fillings at distance 4 or 5. We show that if $M$ is a hyperbolic 3-manifold with a torus boundary component $T_0$, and $r,s$ are two slopes on $T_0$ with $\Delta(r,s) =…

Closed 3-string braids admit many bandings to two-bridge links. By way of the Montesinos Trick, this allows us to construct infinite families of knots in the connected sum of lens spaces L(r,1) # L(s,1) that admit a surgery to a lens space…

For a hyperbolic knot in the 3-sphere, the distance between toroidal surgeries is at most 5, except the figure eight knot. In this paper, we determine all hyperbolic knots that admit two toroidal surgeries with distance 5.