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 $\geq 2$. We will use our particular point of view that the Margulis spacetime is a manifold-with-boundary with an ${\Bbb R}{\sf P}^3$-structure in an essential way. The basic tools are a bordification by a closed ${\Bbb R}{\sf P}^2$-surface with free holonomy group, and the work of Goldman, Labourie, and Margulis on geodesics in the Margulis spacetimes and $3$-manifold topology.

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