Fundamental polyhedra for Margulis space-times

Notes on a paper of Mess

“…Mess goes on to say that "it seems plausible that a complete Lorentz manifold with free fundamental group is diffeomorphic to the interior of a (possibly non-orientable) handlebody", but this question remains open. On the other hand, the cited conjecture of Margulis that a complete Lorentz manifold with finitely generated free fundametal group has discrete and purely hyperbolic linear holonomy has been disproven; Drumm [45] constructs affine deformations of any free Fuchsian group which act properly on Minkowski space.…”

Proper affine actions and geodesic flows of hyperbolic surfaces

“…0 ; V/, we denote the corresponding affine deformation by u . Drumm [13], [15], [16], [12] showed that Mess's necessary condition of noncompactness is sufficient: every noncocompact discrete subgroup of O.2; 1/ 0 admits proper affine deformations. In particular he found an open subset of H 1 .…”

Geodesics in Margulis spacetimes

“…Explicit geometric constructions of these manifolds have been given by Drumm [9,10] and his coauthors [4,5,6,7,11]. …”