807 research outputs found
The universal character ring of the (-2,2m+1,2n)-pretzel link
We explicitly calculate the universal character ring of the
(-2,2m+1,2n)-pretzel link and show that it is reduced for all integers m and n.Comment: Very minor changes. To appear in the International Journal of
Mathematic
On the AJ conjecture for cables of twist knots
We study the AJ conjecture that relates the A-polynomial and the colored
Jones polynomial of a knot in . We confirm the AJ conjecture for
-cables of the -twist knot, for all odd integers satisfying
Comment: Results in Section 3 are corrected. arXiv admin note: text overlap
with arXiv:1111.5258, arXiv:1405.4055; and with arXiv:math/0407521 by other
author
Twisted Alexander polynomials with the adjoint action for some classes of knots
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 formula for the nonabelian Reidemeister torsion of twist knots that is
better than the one in \cite{DHY}.Comment: 9 pages, 1 figure. To appear in Journal of Knot Theory and Its
Ramification
On left-orderability and cyclic branched coverings
In a recent paper Y. Hu has given a sufficient condition for the fundamental
group of the r-th cyclic branched covering of S^3 along a prime knot to be
left-orderable in terms of representations of the knot group. Applying her
criterion to a large class of two-bridge knots, we determine a range of the
integer r>1 for which the r-th cyclic branched covering of S^3 along the knot
is left-orderable.Comment: 9 pages, 1 figur
The strong AJ conjecture for cables of torus knots
The AJ conjecture, formulated by Garoufalidis, relates the A-polynomial and
the colored Jones polynomial of a knot in the 3-sphere. It has been confirmed
for all torus knots, some classes of two-bridge knots and pretzel knots, and
most cabled knots over torus knots. The strong AJ conjecture, formulated by
Sikora, relates the A-ideal and the colored Jones polynomial of a knot. It was
confirmed for all torus knots. In this paper we confirm the strong AJ
conjecture for most cabled knots over torus knots.Comment: 9 page
Volumes of double twist knot cone-manifolds
We give explicit formulae for the volumes of hyperbolic cone-manifolds of
double twist knots, a class of two-bridge knots which includes twist knots and
two-bridge knots with Conway notation . We also study the Riley
polynomial of a class of one-relator groups which includes two-bridge knot
groups.Comment: 11 pages, 1 figur
On left-orderable fundamental groups and Dehn surgeries on knots
We show that the resulting manifold by -surgery on a large class of
two-bridge knots has left-orderable fundamental group if the slope
satisfies certain conditions. This result gives a supporting evidence to a
conjecture of Boyer, Gordon and Watson that relates -spaces and the
left-orderability of their fundamental groups.Comment: Very minor changes. To appear in the Journal of the Mathematical
Society of Japa
Reidemeister torsion and Dehn surgery on twist knots
We compute the Reidemeister torsion of the complement of a twist knot in
and that of the 3-manifold obtained by a Dehn surgery on a twist knot.Comment: 8 pages, 1 figur
Left-orderability for surgeries on twisted torus knots
We show that the fundamental group of the -manifold obtained by
-surgery along the -twisted -torus knot, with
, is not left-orderable if and is
left-orderable if is sufficiently close to .Comment: 6 page
Adjoint twisted Alexander polynomials of genus one two-bridge knots
We give explicit formulas for the adjoint twisted Alexander polynomial and
the nonabelian Reidemeister torsion of genus one two-bridge knots.Comment: 11 page
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