Related papers: Characterizing slopes for $5_2$

The alternating knots, links and twists projected on the $S_2$ sphere were identified with the phase space of a Hamiltonian dynamic system of one degree of freedom. The saddles of the system correspond to the crossings, the edges correspond…

A knot in $S^3$ is topologically slice if it bounds a locally flat disk in $B^4$. A knot in $S^3$ is rationally slice if it bounds a smooth disk in a rational homology ball. We prove that the smooth concordance group of topologically and…

In this paper we classify, up to rigid isotopy, non-singular real rational curves of degrees less than or equal to 6 in a quadric homeomorphic to the 3-sphere. We also study their connections with rigid isotopy classes of real rational…

We classify all the lattices realized as the intersection form of a positive definite four manifold with boundary $S_n^3(K)$ for a knot $K$ in the three sphere and a positive integer $n$ greater than $4g_4(K)+3$. We then use this result to…

We propose a classification of knots in S^1 x S^2 that admit a longitudinal surgery to a lens space. Any lens space obtainable by longitudinal surgery on some knots in S^1 x S^2 may be obtained from a Berge-Gabai knot in a Heegaard solid…

Let X be a norm curve in the SL(2,C)-character variety of a knot exterior M. Let t = || b || / || a || be the ratio of the Culler-Shalen norms of two distinct non-zero classes a, b in H_1(\partial M, Z). We demonstrate that either X has…

Given a simply-connected closed 4-manifold $X$ and a smoothly embedded oriented surface $\Sigma$, various constructions based on Fintushel-Stern knot surgery have produced new surfaces in $X$ that are pairwise homeomorphic to $\Sigma$, but…

For the purposes of this paper, Dehn surgery along a curve K in a 3-manifold M with slope r is `exceptional' if the resulting 3-manifold M_K(r) is reducible or a solid torus, or the core of the surgery solid torus has finite order in the…

This is a companion paper to earlier work of the authors, which proved an integral surgery formula for framed instanton homology. First, we present an enhancement of the large surgery formula, a rational surgery formula for null-homologous…

We introduce a unified framework for counting representations of knot groups into $SU(2)$ and $SL(2, \mathbb{R})$. For a knot $K$ in the 3-sphere, Lin and others showed that a Casson-style count of $SU(2)$ representations with fixed…

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 establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of "Jones slopes" of knots and…

We give a complete classification of the Dehn surgeries on Montesinos knots which yield manifolds with cyclic or finite fundamental groups.

It is known that any contact 3-manifold can be obtained by rational contact Dehn surgery along a Legendrian link L in the standard tight contact 3-sphere. We define and study various versions of contact surgery numbers, the minimal number…

In this paper the 5-dimensional contact SO(3)-manifolds are classified up to equivariant contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that…

Motivated by the L-space conjecture, we investigate various notions of order-detection of slopes on knot manifolds. These notions are designed to characterise when rational homology 3-spheres obtained by gluing compact manifolds along torus…

We show that the resulting manifold by $r$-surgery on a large class of two-bridge knots has left-orderable fundamental group if the slope $r$ satisfies certain conditions. This result gives a supporting evidence to a conjecture of Boyer,…

We prove two arithmetic properties of Dehn surgery points on the canonical component of the $\mathrm{SL}_2(\mathbf{C})$-character variety of the knot $7_4$. The first is that the residue characteristics of the ramified places of the Dehn…

A regular fiber of the Seifert fibering of the Poincar\'e homology sphere admits a Dehn surgery to $L(2,1)\#L(3,2)\#L(5,4)$. We prove that this is the only knot in the Poincar\'e homology sphere with a surgery to a connected sum of more…

In this paper, we study a special family of $(1,1)$ knots called constrained knots, which includes 2-bridge knots in the 3-sphere $S^3$ and simple knots in lens spaces. Constrained knots are parameterized by five integers and characterized…