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arxiv: 1402.4294 · v2 · pith:56TIUUKCnew · submitted 2014-02-18 · 🧮 math.GT

Deformations of reducible representations of knot groups into SL(n,C)

classification 🧮 math.GT
keywords deformationsknotmathbfmathrmreduciblerepresentationsmetabelianalexander
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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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