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

Ben Abdelghani, Leila

doi:10.2140/agt.2010.10.433

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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 $S^{3}$ . 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

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

Volume 10, issue 1 (2010)