Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$

Michael Heusener; Ouardia Medjerab

Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$

Geometric Topology 2015-02-16 v2

Authors: Michael Heusener , Ouardia Medjerab

Abstract

Let $K$ be a knot in $S^3$ and $X$ its complement. We study deformations of non-abelian, metabelian, reducible representations of the knot group $\pi\_1(X)$ into $\mathrm{SL}(n,\mathbf{C})$ which are associated to a simple root of the Alexander polynomial. We prove that certain of these metabelian reducible representations are smooth points of the $\mathrm{SL}(n,\mathbf{C})$ -representation variety and that they have irreducible deformations.

Keywords

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

Cite

@article{arxiv.1402.4294,
  title  = {Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$},
  author = {Michael Heusener and Ouardia Medjerab},
  journal= {arXiv preprint arXiv:1402.4294},
  year   = {2015}
}

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To appear in Mathematica Slovaca

Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$

Abstract

Keywords

Cite

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