Affine Coxeter Extensions of the Two-Holed Projective Plane

Abstract

A Margulis spacetime is a complete flat affine Lorentzian 3-manifold with free fundamental group. Associated to $M$ is a noncompact complete hyperbolic surface $\Sigma$. We study double extensions of ${\pi }_1(M)\cong {\pi }_1(\Sigma )$ when $\Sigma$ is homeomorphic to a projective plane minus two discs. We classify proper actions of this double extension on Minkowski space and show that there exist proper actions that do not admit crooked fundamental domains.

17 pages, 5 figures

References in corpus (3)

• Finite-sided deformation spaces of complete affine 3-manifolds
• Topological tameness of Margulis spacetimes
• Proper affine deformation spaces of two-generator Fuchsian groups