  We study strip deformations of convex cocompact hyperbolic surfaces, defined
by inserting hyperbolic strips along a collection of disjoint geodesic arcs
properly embedded in the surface. We prove that any deformation of the surface
that uniformly lengthens all closed geodesics can be realized as a strip
deformation, in an essentially unique way. The infinitesimal version of this
result gives a parameterization, by the arc complex, of the moduli space of
Margulis spacetimes with fixed convex cocompact linear holonomy. As an
application, we provide a new proof of the tameness of such Margulis spacetimes
M by establishing the Crooked Plane Conjecture, which states that M admits a
fundamental domain bounded by piecewise linear surfaces called crooked planes.
The noninfinitesimal version gives an analogous theory for complete anti-de
Sitter 3-manifolds.
