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

Michael Heusener; Ouardia Medjerab

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arXiv · 1402.4294

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

Michael Heusener·Ouardia Medjerab

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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.

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BibTeX RIS

Michael Heusener, Ouardia Medjerab. 2014-02-18. Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$. https://arxiv.org/abs/1402.4294

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