Related papers: Reidemeister torsion and Dehn surgery on twist kno…

We calculate the twisted Alexander polynomial with the adjoint action for torus knots and twist knots. As consequences of these calculations, we obtain the formula for the nonabelian Reidemeister torsion of torus knots in \cite{Du} and a…

We study the asymptotic behavior of the Witten-Reshetikhin-Turaev invariant associated with the square of the $n$-th root of unity with odd $n$ for a Seifert fibered space obtained by an integral Dehn surgery along a torus knot. We show…

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 determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL(2;C)-representations of the graph manifold are…

We introduce the notion of round surgery diagrams in $S^3$ for representing 3-manifolds similar to Dehn surgery diagrams. We give a correspondence between a certain class of round surgery diagrams and Dehn surgery diagrams for 3-manifolds.…

For a knot $K$ with $\Delta_K(t)\doteq t^2-3t+1$ in a homology $3$-sphere, let $M$ be the result of $2/q$-surgery on $K$. We show that appropriate assumptions on the Reidemeister torsion and the Casson-Walker-Lescop invariant of the…

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 that on any hyperbolic knot in $S^3$ there is at most one non-integral Dehn surgery which yields a manifold containing an incompressible torus.

Given a knot K in the three-sphere, we address the question: which Dehn surgeries on K bound negative-definite four-manifolds? We show that the answer depends on a number m(K), which is a smooth concordance invariant. We study the…

As a generalization of a classical result on the Alexander polynomial for fibered knots, we show in this paper that the Reidemeister torsion associated to a certain representation detects fiberedness of knots in the three sphere.

Ballinger et al. have determined the list of all prism manifolds that are possibly realizable by Dehn surgeries on knots in $S^3$. In this paper, we explicitly find braid words of primitive/Seifert-fibered knots on which surface slope…

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…

This paper gives an explicit formula for the SL_2(C)-non-abelian Reidemeister torsion as defined in [Dub06] in the case of twist knots. For hyperbolic twist knots, we also prove that the non-abelian Reidemeister torsion at the holonomy…

We present new lower bounds on the complexity of Dehn surgery manifolds of knots, using our recent result on the Cheeger-Gromov rho invariants and triangulations. As an application, we give explicit examples of closed hyperbolic 3-manifolds…

A generalized torsion element is a non-trivial element such that some non-empty finite product of its conjugates is the identity. We construct a generalized torsion element of the fundamental group of a 3-manifold obtained by Dehn surgery…

In this paper we describe braid equivalence for knots and links in a 3-manifold $M$ obtained by rational surgery along a framed link in $S^3$. We first prove a sharpened version of the Reidemeister theorem for links in $M$. We then give…

We give an explicit formula for the adjoint Reidemeister torsion of two-bridge knots and prove that the adjoint Reidemeister torsion satisfies a certain type of vanishing identities.

Given a hyperbolic 3-manifold with torus boundary, we bound the change in volume under a Dehn filling where all slopes have length at least 2\pi. This result is applied to give explicit diagrammatic bounds on the volumes of many knots and…

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 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…