On invertible generating pairs of fundamental groups of graph manifolds

We study invertible generating pairs of fundamental groups of graph manifolds, that is, pairs of elements (g,h) for which the map g --> g^{-1}, h --> h^{-1} extends to an automorphism. We show in particular that a graph manifold is of Heegaard genus 2 if and only if its fundamental group has an invertible generating pair.Comment: This is the version published by Geometry & Topology Monographs on 29 April 200

Nielsen equivalence in a class of random groups

We show that for every $n\ge 2$ there exists a torsion-free one-ended word-hyperbolic group $G$ of rank $n$ admitting generating $n$-tuples $(a_1,\ldots ,a_n)$ and $(b_1,\ldots ,b_n)$ such that the $(2n-1)$-tuples $$(a_1,\ldots ,a_n, \underbrace{1,\ldots ,1}_{n-1 \text{times}})\hbox{ and }(b_1,\ldots, b_n, \underbrace{1,\ldots ,1}_{n-1 \text{times}})$$ are not Nielsen-equivalent in $G$. The group $G$ is produced via a probabilistic construction.Comment: 34 pages, 2 figures; a revised final version, to appear in the Journal of Topolog

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

Central Stars of Planetary Nebulae: New spectral classifications and catalogue

Context. There are more than 3000 true and probable known Galactic Planetary Nebulae (PNe), but only for 13% of them there is central star spectroscopic information available. Aims. To contribute to the knowledge of central stars of planetary nebulae and star evolution. Methods. We undertook a spectroscopic survey of central stars of PNe in low resolution and compiled a large list of central stars for which information was dispersed in the literature. Results. We complete a catalogue of 492 true and probable CSPN and we provide a preliminary spectral classification for 45 central star of PNe, This made it possible to update the proportion of CSPN with atmosphere poor in hydrogen with regard to the whole in at least 30% and contribute with statistical information that allow to infer the origin of H-poor stars.Comment: 19 pages, 1 figure, accepted to be published in A&A (October 24, 2010

Kleinian groups and the rank problem

We prove that the rank problem is decidable in the class of torsion-free word-hyperbolic Kleinian groups. We also show that every group in this class has only finitely many Nielsen equivalence classes of generating sets of a given cardinality.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper12.abs.htm