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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

DOI: 10.2140/agt.2010.10.433
Abstract

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.

Keywords

knot group, reducible representation, representation space, character variety
Mathematical Subject Classification

Primary: 57M25, 57M27
References
Publication

Received: 24 March 2009
Revised: 6 November 2009
Accepted: 1 December 2009
Published: 3 March 2010
Authors
Leila Ben Abdelghani
Département de Mathématiques
Faculté des Sciences de Monastir
Route de l'Environnement
5000 Monastir
Tunisie