On the twisted Alexander polynomial for metabelian representations into SL_2(C)

摘要

We observe the twisted Alexander polynomial for metabelian representations of knot groups into SL_2(C) and study relations to the characterizations of metabelian representations in the character varieties. We give a factorization of the twisted Alexander polynomial for irreducible metabelian representations with the adjoint action on sl_2(C), in which the Alexander polynomial and the twisted Alexander polynomial appear as factors. We also show several explicit examples.