Related papers: Characterizing slopes for $5_2$

We classify which positive integral surgeries on positive torus knots bound rational homology balls. Additionally, for a given knot K we consider which cables K(p,q) admit integral surgeries that bound rational homology balls. For such…

In this paper we study rational real algebraic knots in $\R P^3$. We show that two real algebraic knots of degree $\leq5$ are rigidly isotopic if and only if their degrees and encomplexed writhes are equal. We also show that any irreducible…

A knot in $S^3$ is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot concordance group. In particular, our examples are all…

Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since Dehn surgeries on knots in $S^3$ can produce large families of…

Surgery on a knot in $S^3$ is said to be an alternating surgery if it yields the double branched cover of an alternating link. The main theoretical contribution is to show that the set of alternating surgery slopes is algorithmically…

Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We disprove this conjecture by constructing pairs of distinct…

We provide a new obstruction for a rational homology 3-sphere to arise by Dehn surgery on a given knot in the 3-sphere. The obstruction takes the form of an inequality involving the genus of the knot, the surgery coefficient, and a count of…

In this paper, we define a new algebro-geometric invariant of 3-manifolds resulting from the Dehn surgery along a hyperbolic knot complement in S^3. We establish a Casson type invariant for these 3-manifolds. In the last section, we…

We show some computations on representations of the fundamental group in SL(2;C) and Reidemeister torsion for a homology 3-sphere obtained by Dehn surgery along the figure-eight knot. This is the second version. We recorrected several…

Let r_m and r_M be the least and greatest finite boundary slopes of a hyperbolic knot K in S^3. We show that any cyclic surgery slopes of K must lie in the interval (r_m - 1/2, r_M + 1/2).

Berge in [1] defined doubly primitive knots, which yield lens spaces by Dehn surgery. At the same paper he listed the knots into several types. In this paper we will prove the list is complete when $\tau>1$. The invariant $\tau$ is a…

Suppose $K$ is a hyperbolic knot in a solid torus $V$ intersecting a meridian disk $D$ twice. We will show that if $K$ is not the Whitehead knot and the frontier of a regular neighborhood of $K \cup D$ is incompressible in the knot…

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…

For any hyperbolic twist 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 $r$ satisfies the inequality $0\le r \le 4$.

In this paper, we provide an explicit construction of continuous paths of $\mathrm{SL}_2(\mathbb R)$-representations of the knot groups of $(-2,3,2n+1)$-pretzel knots. As an application, we show that the fundamental group of the…

We prove that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). For hyperbolic integer homology spheres this comes with the definition,…

We classify Dehn surgeries on (p,q,r) pretzel knots resulting in a manifold M(s) having cyclic fundamental group and analyze those leading to a finite fundamental group. The proof uses the theory of cyclic and finite surgeries developed by…

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

Previous work of the authors establishes a criterion on the fundamental group of a knot complement that determines when Dehn surgery on the knot will have a fundamental group that is not left-orderable. We provide a refinement of this…

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…