Mapping class group orbit closures for non-orientable surfaces

2021/10/06 by Viveka Erlandsson, Matthieu Gendulphe, Erlandsson, Viveka +5
Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2110.02644

openalex publication_date 2021/10/06 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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 and \mathcal P\mathcal M\mathcal 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 of the set of weighted two-sided curves.

Citations

• Paysage Systolique Des Surfaces Hyperboliques Compactes De Caracteristique -1
• What's wrong with the growth of simple closed geodesics on nonorientable hyperbolic surfaces

Related

• A finite presentation of the mapping class group of an oriented surface
• Mapping class groups of non-orientable surfaces for beginners
• A spine for the decorated Teichmüller space of a punctured non-orientable surface
• The mapping class group orbits in the framings of compact surfaces
• A new boundary of the mapping class group