Search results for "Skein relation"
showing 5 items of 5 documents
On orderability of fibred knot groups
2003
It is known that knot groups are right-orderable, and that many of them are not bi-orderable. Here we show that certain bred knots in S 3 (or in a homology sphere) do have bi-orderable fundamental group. In particular, this holds for bred knots, such as 41, for which the Alexander polynomial has all roots real and positive. This is an application of the construction of orderings of groups, which are moreover invariant with respect to a certain automorphism.
Non-equivalent hyperbolic knots
2002
We construct, for each integer n 3, pairs of non-equivalent hyperbolic knots with the same 2fold and n-fold cyclic branched covers. We also discuss necessary conditions for such pairs of knots to exist. 2001 Elsevier Science B.V. All rights reserved. MSC: primary 57M25; secondary 57M12, 57M50
INVOLUTIONS ON KNOT GROUPS AND VARIETIES OF REPRESENTATIONS IN A LIE GROUP
2002
We prove the existence of a rationalisation [Formula: see text] of a classical or high-dimensional knot group Π which admits an involution if the Alexander polynomials of the knot are reciprocal. Using the group [Formula: see text] and its involution, we study the local structure, in the neighbourhood of an abelian representation, of the space of representation of the knot group Π in a a Lie group. We apply these results to the groups of classical prime knots up to 10 crossings.
HOMFLY-PT skein module of singular links in the three-sphere
2012
For a ring R, we denote by [Formula: see text] the free R-module spanned by the isotopy classes of singular links in 𝕊3. Given two invertible elements x, t ∈ R, the HOMFLY-PT skein module of singular links in 𝕊3 (relative to the triple (R, t, x)) is the quotient of [Formula: see text] by local relations, called skein relations, that involve t and x. We compute the HOMFLY-PT skein module of singular links for any R such that (t-1 - t + x) and (t-1 - t - x) are invertible. In particular, we deduce the Conway skein module of singular links.
Conway irreducible hyperbolic knots with two common covers
2005
International audience; For each pair of coprime integers n > m ≥ 2 we construct pairs of non equivalent Conway irreducible hyperbolic knots with the same n-fold and m-fold cyclic branched covers.