Generating pairs of 2-bridge knot groups

We study Nielsen equivalence classes of generating pairs of Kleinian groups and HNN-extensions. We establish the following facts: - Hyperbolic 2-bridge knot groups have infinitely many Nielsen classes of generating pairs. - For any natural number N there is a closed hyperbolic 3-manifold whose fundamental group has N distinct Nielsen classes of generating pairs. - Two pairs of elements of a fundamental group of an HNN-extension are Nielsen equivalent iff they are so for the obvious reasons.Comment: Final version to appear in Geometriae Dedicat

Deformations of reducible representations of 3-manifold groups into PSL_2(C)

Let M a 3-manifold with torus boundary which is a rational homology circle. We study deformations of reducible representations of p_1(M) into PSL_2(C) associated to a simple zero of the twisted Alexander polynomial. We also describe the local structure of the representation and character varieties.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-40.abs.htm

Holomorphic volume forms on representation varieties of surfaces with boundary

For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the other one is the power of the Atiyah-Bott-Goldman-Narasimhan symplectic form. We introduce an holomorphic volume form on the space of representations of the circle, so that, for surfaces with boundary, it appears as peripheral term in the generalization of Witten's formula. We compute explicit volume and symplectic forms for some simple surfaces and for the Lie group SLN (C).Pour les surfaces hyperboliques fermées et orientées, une formule de Witten établit une égalité entre deux formes de volume sur l'espace de représentations des groupes de surface dans un groupe de Lie semi-simple. Une de ces formes est une torsion de Reidemeister, l'autre est la forme de volume canoniquement associée à la forme symplectique d'Atiyah-Bott-Goldman-Narasimhan. Nous introduisons une forme de volume holomorphe sur l'espace des représentations du cercle, de sorte que, pour les surfaces à bord, elle apparaisse comme terme périphérique dans la généralisation de la formule de Witten. Pour certaines surfaces simples et pour le groupe de Lie SLN (C) nous calculons explicitement les formes volume et les formes symplectiques

Cohomological characterization of relative hyperbolicity and combination theorem

We give a cohomological characterization of Gromov relative hyperbolicity. As an application we prove a converse to the combination theorem for graphs of relatively hyperbolic groups given in [9]. We build upon and follow the ideas of the work of S. M. Gersten [11] about the same topics in the classical Gromov hyperbolic setting