#### Volume 10, issue 1 (2010)

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Tangent cones and local geometry of the representation and character varieties of knot groups

### Leila Ben Abdelghani

Algebraic & Geometric Topology 10 (2010) 433–463
##### Abstract

Let $K$ be a knot in the $3$–sphere ${S}^{3}$. We calculate explicitly the tangent cone to the representation variety at an abelian representation which corresponds to a double root of the Alexander polynomial. We also describe the local structure of the representation and character varieties.

##### Keywords
knot group, reducible representation, representation space, character variety
##### Mathematical Subject Classification 2000
Primary: 57M25, 57M27