Isometries of Lorentz surfaces and convergence groups

Abstract

We study the isometry group of a globally hyperbolic spatially compact Lorentz surface. Such a group acts on the circle, and we show that when the isometry group acts non properly, the subgroups of $\mathrm{Diff}({\mathbb{S}}^1)$ obtained are semi conjugate to subgroups of finite covers of $\mathrm{PSL}(2,\mathbb{R})$ by using convergence groups. Under an assumption on the conformal boundary, we show that we have a conjugacy in $\mathrm{Homeo}({\mathbb{S}}^1)$.

39 pages, 7 figures

References in corpus (1)

• On smooth Cauchy hypersurfaces and Geroch's splitting theorem