6533b827fe1ef96bd1286d7a
RESEARCH PRODUCT
On orderability of fibred knot groups
Bernard PerronDale Rolfsensubject
CombinatoricsAlgebraHOMFLY polynomialKnot invariantGeneral MathematicsSkein relationAlexander polynomialKnot polynomialTricolorabilityMathematics::Geometric TopologyMathematicsKnot theoryFinite type invariantdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-07-01 | Mathematical Proceedings of the Cambridge Philosophical Society |