TOPOLOGICAL TAMENESS OF MARGULIS SPACETIMES

Abstract

We show that Margulis spacetimes without parabolic holonomy elements 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 >= 2. We will use our particular point of view that the Margulis spacetime is a manifold-with-boundary with an RP3-structure in an essential way. The basic tools are a bordification by a closed RP2-surface with free holonomy group, and the work of Goldman, Labourie, and Margulis on geodesics in the Margulis spacetimes and 3-manifold topology.