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