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

Ben Abdelghani, Leila¹

¹Département de Mathématiques, Faculté des Sciences de Monastir, Route de l’Environnement, 5000 Monastir, Tunisie

Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 433-463

Résumé

Let K be a knot in the 3–sphere S3. 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.

Détail

DOI : 10.2140/agt.2010.10.433

Keywords: knot group, reducible representation, representation space, character variety

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