Tameness of Margulis space-times with parabolics

Abstract

Let E be a flat Lorentzian space of signature (2, 1). A Margulis space-time is a noncompact complete Lorentz flat 3-manifold E/Gamma with a free holonomy group Gamma of rank g, g >= 2. We consider the case when Gamma contains a parabolic element. We obtain a characterization of proper F-actions in terms of Margulis and Charette-Drumm invariants. We show that E/Gamma is homeomorphic to the interior of a compact handlebody of genus g generalizing our earlier result. Also, we obtain a bordification of the Margulis space-time with parabolics by adding a real projective surface at infinity giving us a compactification as a manifold relative to parabolic end neighborhoods. Our method is to estimate the translational parts of the affine transformation group and use some 3-manifold topology.