Higher dimensional twisted Alexander polynomials for metabelian representations

Anh T. Tran; Yoshikazu Yamaguchi

Higher dimensional twisted Alexander polynomials for metabelian representations

Geometric Topology 2016-08-22 v1

Authors: Anh T. Tran , Yoshikazu Yamaguchi

Abstract

We study the asymptotic behavior of the twisted Alexander polynomial for the sequence of SL(n ,C)-representations induced from an irreducible metabelian SL(2, C)-representation of a knot group. We give the limits of the leading coefficients in the asymptotics of the twisted Alexander polynomial and related Reidemeister torsion. The concrete computations for all genus one two-bridge knots are also presented.

Keywords

alexander polynomial asymptotic analysis knot theory

Cite

@article{arxiv.1608.05525,
  title  = {Higher dimensional twisted Alexander polynomials for metabelian representations},
  author = {Anh T. Tran and Yoshikazu Yamaguchi},
  journal= {arXiv preprint arXiv:1608.05525},
  year   = {2016}
}

Comments

12 pages, 1 figure

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