On the twisted Alexander polynomial for metabelian representations into SL(2, C)

2011/01/20 by Yoshikazu Yamaguchi, Yamaguchi, Yoshikazu
Mathematics · #57M05 #57M12 #57M27 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1101.3989

openalex publication_date 2011/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Higher dimensional twisted Alexander polynomials for metabelian representations
• Deformations of metabelian representations of knot groups into SL(3,ℂ)
• Twisted Alexander polynomials and character varieties of 2-bridge knot groups
• Twisted Alexander polynomials of 2-bridge knots associated to metabelian representations
• Deformations of reducible representations of knot groups into\n \SL(n,\C)