Twisted Alexander invariants of knot group representations II; computation and duality

2020/04/07 by Nosaka, Takefumi
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2004.03255

Abstract

Given a homomorphism from a link group to a group, we introduce a K₁-class in another way, which is a generalization of the 1-variable Alexander polynomial. We compare the K₁-class with K₁-classes in \citeNos and with Reidemeister torsions. As a corollary, we show a relation to Reidemeister torsions of finite cyclic covering spaces, and show reciprocity in some senses.

Related

• Twisted Alexander invariants of knot group representations
• Twisted Alexander polynomials of knots associated to the regular representations of finite groups
• Twisted Alexander polynomials of genus one two-bridge knots
• Twisted Alexander polynomials, character varieties and Reidemeister torsion of double branched covers
• Alexander-Lin twisted polynomials