0000000000876530
AUTHOR
Leila Ben Abdelghani
INVOLUTIONS ON KNOT GROUPS AND VARIETIES OF REPRESENTATIONS IN A LIE GROUP
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.
Varieties of representations of virtual knot groups in SL2(C)
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.