Mapping class group orbit closures for non-orientable surfaces

Abstract

Let S be a connected non-orientable surface with negative Euler characteristic and of finite type. We describe the possible closures in $$\mathcal M\mathcal L$$ M L and $$\mathcal P\mathcal M\mathcal L$$ P M L of the mapping class group orbits of measured laminations, projective measured laminations and points in Teichmüller space. In particular we obtain a characterization of the closure in $$\mathcal M\mathcal L$$ M L of the set of weighted two-sided curves.