Search results for "Knot complement"

showing 3 items of 3 documents

A knot without tritangent planes

1991

We show, with computations aided by a computer, that the (3,2)-curve on some standard torus (which topologically is the trefoil knot) has no tritangent planes, thus answering in the negative a conjecture of M. H. Freedman.

CombinatoricsKnot complementKnot invariantSeifert surfaceQuantum invariantGeometry and TopologyTricolorabilityMathematics::Geometric TopologyTrefoil knotMathematicsKnot (mathematics)Pretzel linkGeometriae Dedicata
researchProduct

A knot without triple bitangency

1997

It is proved that certain trefoil knot has not triple bitangency, answering thus in the negative a conjecture of S. Izumiya and W. L. Marar.

CombinatoricsKnot complementMathematics::Algebraic GeometryConjectureGeometry and TopologyMathematics::Geometric TopologyKnot (mathematics)Pretzel linkTrefoil knotMathematicsJournal of Geometry
researchProduct

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.

Knot complementAlgebraPure mathematicsAlgebra and Number TheoryKnot invariantKnot groupQuantum invariantSkein relationTricolorabilityMathematics::Geometric TopologyMathematicsKnot theoryTrefoil knotJournal of Knot Theory and Its Ramifications
researchProduct