Given a homomorphism from a knot group to a fixed group, we introduce an element of a -group, which is a generalization of (twisted) Alexander polynomials. We compare the -class with other Alexander polynomials. In terms of semi-local rings, we compute the -classes of some knots and show their non-triviality. We also introduce metabelian Alexander polynomials.
"Twisted Alexander Invariants of Knot Group Representations." Tokyo J. Math. 45 (1) 215 - 236, June 2022. https://doi.org/10.3836/tjm/1502179346