Parametrisation of decorated Margulis spacetimes using strip deformations
摘要
Danciger-Guéritaud-Kassel parametrised the moduli space of Margulis spacetimes, with a fixed convex cocompact linear part. The parametrisation is done by gluing infinitesimal hyperbolic strips along a family of embedded, pairwise disjoint finite geodesic segments of the hyperbolic surface that decompose it into topological disks. We generalise this result to complete finite-area crowned hyperbolic surfaces with their spikes decorated with horoballs, by using hyperbolic as well as parabolic strips. This gives a parametrisation of Margulis spacetimes, decorated with finitely many pairwise disjoint affine light-like lines, called photons.