Deformations of metabelian representations of knot groups into $SL(3,\mathbb{C})$

Leila Ben Abdelghani; Michael Heusener; Hajer Jebali

Deformations of metabelian representations of knot groups into $SL(3,\mathbb{C})$

Geometric Topology 2008-10-16 v3

Authors: Leila Ben Abdelghani , Michael Heusener , Hajer Jebali

Abstract

Let K be a knot in $S^3$ and $X$ its complement. We study deformations of reducible metabelian representations of the knot group $\pi_1(X)$ into $SL(3,\mathbb{C})$ which are associated to a double root of the Alexander polynomial. We prove that these reducible metabelian representations are smooth points of the representation variety and that they have irreducible non metabelian deformations.

Keywords

knot groups metabelian representations deformations SL(3,C) Alexander polynomial representation variety

Cite

@article{arxiv.0710.3511,
  title  = {Deformations of metabelian representations of knot groups into $SL(3,\mathbb{C})$},
  author = {Leila Ben Abdelghani and Michael Heusener and Hajer Jebali},
  journal= {arXiv preprint arXiv:0710.3511},
  year   = {2008}
}

Comments

Accepted in Journal of Knot Theory and Its Ramifications

Deformations of metabelian representations of knot groups into $SL(3,\mathbb{C})$

Abstract

Keywords

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