Related papers: Boundary slopes (nearly) bound exceptional slopes

Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in $S^3$ do not admit purely cosmetic surgeries. In this article, we…

Which slopes can or cannot appear as Seifert fibered slopes for hyperbolic knots in the 3-sphere S^3? It is conjectured that if r-surgery on a hyperbolic knot in S^3 yields a Seifert fiber space, then r is an integer. We show that for each…

A slope $\frac pq$ is called a characterizing slope for a given knot $K_0\subset S^3$ if whenever the $\frac pq$--surgery on a knot $K\subset S^3$ is homeomorphic to the $\frac pq$--surgery on $K_0$ via an orientation preserving…

We prove that there are exactly $6$ Nil Seifert fibred spaces which can be obtained by Dehn surgeries on non-trefoil knots in $S^3$, with $\{60, 144, 156, 288, 300\}$ as the exact set of all such surgery slopes up to taking the mirror…

We prove two conjectures of C. Gordon. We show that the maximal number of exceptional Dehn surgeries on a 1-cusped hyperbolic 3-manifold is 10, and that the maximal intersection number between exceptional slopes is 8. The proof uses a…

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…

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…

We will classify all exceptional Dehn surgeries on 2-bridge knots according to whether they produce reducible, toroidal, or small Seifert fibered manifolds.

A slope $p/q$ is said to be characterizing for a knot $K$ if the homeomorphism type of the $p/q$-Dehn surgery along $K$ determines the knot up to isotopy. Extending previous work of Lackenby and McCoy on hyperbolic and torus knots…

We show that for certain hyperbolic 3-manifolds, all boundary slopes are slopes of immersed incompressible surfaces, covered by incompressible embeddings in some finite cover. The manifolds include hyperbolic punctured torus bundles and…

A surgery on a knot in 3-sphere is called SU(2)-cyclic if it gives a manifold whose fundamental group has no non-cyclic SU(2) representations. Using holonomy perturbations on the Chern-Simons functional, we prove that the distance of two…

In this paper, we give a complete classification of exceptional Dehn surgeries on a component of a hyperbolic two-bridge link in the 3-sphere.

Using work of Ozsvath and Szabo, we show that if a nontrivial knot in S^3 admits a lens space surgery with slope p, then p <= 4g+3, where g is the genus of the knot. This is a close approximation to a bound conjectured by Goda and…

By considering non-orientable surfaces in the surgered manifolds, we show that the 10/3- and -10/3-Dehn surgeries on the 2-bridge knot $9_{27} = S(49,19)$ are not cosmetic, i.e., they give mutually non-homeomorphic manifolds. The knot is…

We use sutured manifold theory, essential laminations and essential branched surfaces to establish the upper bounds of distances between certain types of nonsimple Dehn surgery slopes. This is the revised version of an earlier preprint {\it…

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…

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…

Using the rational surgery formula for the Casson--Walker--Lescop invariant of links in the $3$-sphere, we show that any null-homologous knot in a rational homology sphere admits at most two pairs of integral purely cosmetic surgeries. We…

Suppose $\alpha$ and $R$ are disjoint simple closed curves in the boundary of a genus two handlebody $H$ such that $H[R]$ embeds in $S^3$ as the exterior of a hyperbolic knot $k$(thus, $k$ is a tunnel-number-one knot), and $\alpha$ is…

We study Dehn surgeries on null-homotopic knots that yield fibred $3$--manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai's theory of sutured manifold decomposition. Such surgeries…