Search results for "Knot polynomial"

showing 2 items of 2 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.

CombinatoricsAlgebraHOMFLY polynomialKnot invariantGeneral MathematicsSkein relationAlexander polynomialKnot polynomialTricolorabilityMathematics::Geometric TopologyMathematicsKnot theoryFinite type invariantMathematical Proceedings of the Cambridge Philosophical Society
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Varieties of representations of virtual knot groups in SL2(C)

2002

Abstract We study the local structure of the variety of representations of a virtual knot group in SL 2 ( C ) near an abelian representation ρ 0 . To such a representation is attached a complex number ω and there are three cases. If ω and ω −1 are not roots of the Alexander polynomial, there are only abelian representations around ρ 0 . If ω is a root and ω −1 is not, there are only reducible representations. If both ω and ω −1 are roots and certain homological conditions hold, there are irreducible representations.

Pure mathematicsInduced representationQuantum invariantAlexander polynomialKnot polynomialVirtual knotKnot theoryAlgebraKnot invariantRepresentation theory of SUVirtual knot groupsRepresentation spacesGeometry and TopologyMathematicsTopology and its Applications
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