On reciprocality of twisted Alexander invariants

Abstract

Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for which the twisted Reidemeister torsion is not reciprocal.

10 pages, no figures

References in corpus (2)

• Twisted Alexander polynomials of periodic knots
• Symplectic S^1 x N^3, subgroup separability, and vanishing Thurston norm

Cited by in corpus (12)

• Twisted Alexander polynomials of 2-bridge knots for parabolic representations
• Representations of knot groups into ${\mathrm{SL}}_n(\mathbf{C})$ and twisted Alexander polynomials
• The L^2-Alexander torsion of 3-manifolds
• Twisted Alexander invariant and non-abelian Reidemeister torsion for hyperbolic three-dimensional manifolds with cusps
• Poincaré duality and degrees of twisted Alexander polynomials
• Three flavors of twisted invariants of knots
• Twisted Alexander polynomials of hyperbolic knots
• Twisted Alexander polynomials and character varieties of 2-bridge knot groups
• The taut polynomial and the Alexander polynomial
• Profinite rigidity for twisted Alexander polynomials
• Thurston norm via Fox calculus
• Twisting Alexander Invariants with Periodic Representations