Related papers: Left-orderablity for surgeries on $(-2,3,2s+1)$-pr…

Let K be a non-trivial knot in the 3-sphere and let Y(r) be the 3-manifold obtained by surgery on K with surgery-coefficient a rational number r. We show that there is a homomorphism from the fundamental group of Y(r) to SU(2) with…

We describe a method to compute the Culler-Shalen seminorms of a knot, using the (-3,3,4) pretzel knot as an illustrative example. We deduce that the SL2(C)-character variety of this knot consists of three algebraic curves and that it…

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 show that all pretzel knots satisfy the (purely) cosmetic surgery conjecture, i.e. Dehn surgeries with different slopes along a pretzel knot provide different oriented three-manifolds.

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 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…

We show that a knot has a non left-orderable surgery if the knot group admits a generalized Baumslag-Solitar relator and satisfies certain conditions on a longitude of the knot. As an application, it is shown that certain positively twisted…

Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if the resulting 3--manifold K(r) of the surgery has left-orderable fundamental group, and an r-surgery on K is called an L-space surgery if K(r) is an L-space. A…

Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in $S^3$, we show that the two surgery slopes must…

In this paper, we study the Riley polynomial of double twist knots with higher genus. Using the root of the Riley polynomial, we compute the range of rational slope $r$ such that $r$-filling of the knot complement has left-orderable…

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…

A Dehn surgery on a knot $K$ in $S^3$ is exceptional if it produces a reducible, toroidal or Seifert fibred manifold. It is known that a large arborescent knot admits no such surgery unless it is a type II arborescent knot. The main theorem…

We show that the 3-fold cyclic branched cover of any genus 2 two-bridge knot $K_{[-2q,2s,-2t,2l]}$ is an L-space and its fundamental group is not left-orderable. Therefore the family of 3-fold cyclic branched cover of any genus 2 two-bridge…

Let K be a (2p,q)-torus knot and M_n is a 3-manifold obtained by 1/n-Dehn surgery along K. We consider a polynomial whose zeros are the inverses of the Reideimeister torsion of M_n for SL(2;C)-irreducible representations. Johnson gave a…

We use the combinatorial techniques of graphs of intersection to study reducible Dehn surgeries on knots in the three-sphere. In particular, in the event that a reducible surgery on a knot K in the three-sphere of slope r produces a…

We establish a necessary condition that an automorphism of a nontrivial finitely generated bi-orderable group can preserve a bi-ordering: at least one of its eigenvalues, suitably defined, must be real and positive. Applications are given…

We show that the fundamental group of the double branched cover of an infinite family of homologically thin, non-quasi-alternating knots is not left-orderable, giving further support for a conjecture of Boyer, Gordon, and Watson that an…

For some families of two-bridge knots, including double-twist knots with genus at least four, we determine precisely the set of integers $n>1$ such that the fundamental group of the $n$-fold cyclic branched cover of the 3-sphere along these…

In an earlier paper, we used the absolute grading on Heegaard Floer homology to give restrictions on knots in $S^3$ which admit lens space surgeries. The aim of the present article is to exhibit stronger restrictions on such knots, arising…

We provide an alternative proof of a sufficient condition for the fundamental group of the $n^{th}$ cyclic branched cover of $S^3$ along a prime knot $K$ to be left-orderable, which is originally due to Boyer-Gordon-Watson. As an…