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arxiv: 0710.3511 · v3 · submitted 2007-10-18 · 🧮 math.GT

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

classification 🧮 math.GT
keywords metabeliandeformationsknotrepresentationsmathbbreduciblealexanderassociated
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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.

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