6533b839fe1ef96bd12a595c

RESEARCH PRODUCT

INVOLUTIONS ON KNOT GROUPS AND VARIETIES OF REPRESENTATIONS IN A LIE GROUP

Leila Ben AbdelghaniDaniel Lines

subject

Knot complementAlgebraPure mathematicsAlgebra and Number TheoryKnot invariantKnot groupQuantum invariantSkein relationTricolorabilityMathematics::Geometric TopologyMathematicsKnot theoryTrefoil knot

description

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.

yearjournalcountryeditionlanguage
2002-02-01Journal of Knot Theory and Its Ramifications
https://doi.org/10.1142/s0218216502001482