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RESEARCH PRODUCT

On orderability of fibred knot groups

Bernard PerronDale Rolfsen

subject

CombinatoricsAlgebraHOMFLY polynomialKnot invariantGeneral MathematicsSkein relationAlexander polynomialKnot polynomialTricolorabilityMathematics::Geometric TopologyMathematicsKnot theoryFinite type invariant

description

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.

https://doi.org/10.1017/s0305004103006674