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

Leila Ben Abdelghani; Michael Heusener; Hajer Jebali

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arXiv · 0710.3511

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

Leila Ben Abdelghani·Michael Heusener·Hajer Jebali

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Abstract

Let K be a knot in $S^3$ and $X$ its complement. We study deformations of reducible metabelian representations of the knot group $π_1(X)$ 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.

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BibTeX RIS

Leila Ben Abdelghani, Michael Heusener, Hajer Jebali. 2008-10-16. Deformations of metabelian representations of knot groups into $SL(3,\mathbb{C})$. https://arxiv.org/abs/0710.3511

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