Dynamics and topology on 3-dimensional Lorentz manifolds

A classical result of Myers and Steenrod states that the isometry group of a compact Riemannian manifold is
a compact Lie transformation group. Also classical is the fact  that this compactness property fails for general
pseudo-Riemannian manifolds, allowing interesting dynamics for the group of isometries.
In this talk, we will be interested by the topological, and dynamical consequences of  the noncompactness of
the isometry group.  We will especially focus  on the case of Lorentz manifolds, and we will present a
complete topological classification of 3-dimensional closed Lorentz manifolds having a noncompact isometry
group.