Topological tameness of Margulis spacetimes

Abstract

We show that Margulis spacetimes without parabolic holonomy are topologically tame. A Margulis spacetime is the quotient of the $3$-dimensional Minkowski space by a free proper isometric action of the free group of rank $\ge 2$. We will use our particular point of view that the Margulis spacetime is a manifold-with-boundary with an $\mathbb{R}{P}^3$-structure in an essential way. The basic tools are a bordification by a closed $\mathbb{R}{P}^2$-manifold with free holonomy group, and the work of Goldman, Labourie, and Margulis on geodesics in the Margulis spacetimes and $3$-manifold topology.

51 pages, 6 figures. Corrected a few typos (The 6th version of "The topological and geometrical finiteness of complete flat Lorentzian 3-manifolds with free fundamental groups" arXiv:1204.5308v1 [math.GT])

References in corpus (4)

• Tameness of hyperbolic 3-manifolds
• Finite-sided deformation spaces of complete affine 3-manifolds
• End reductions, fundamental groups, and covering spaces of irreducible open 3-manifolds
• Mining Attribute-based Access Control Policies

Cited by in corpus (3)

• Proper affine deformation spaces of two-generator Fuchsian groups
• Affine Coxeter Extensions of the Two-Holed Projective Plane
• Margulis spacetimes via the arc complex