Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page

Realising end invariants by limits of minimally parabolic, geometrically finite groups

We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is an algebraic limit of minimally parabolic, geometrically finite Kleinian groups which has exactly that homeomorphism type and end invariants. This shows that the Bers-Sullivan-Thurston density conjecture follows from Marden's conjecture proved by Agol, Calegari-Gabai combined with Thurston's uniformisation theorem and the ending lamination conjecture proved by Minsky, partially collaborating with Masur, Brock and Canary.Comment: fourth version: Introduction rewritten; some arguments in Sec. 5 and 6 clarified