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

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

2007-10-18

arxiv.org/abs/0710.3511v3

Mathematics

Geometric Topology

Accepted in Journal of Knot Theory and Its Ramifications

Scientific paper

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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