Mapping class group orbit closures for non-orientable surfaces

TL;DR

This paper characterizes the closures of mapping class group orbits of measured laminations and points in Teichmüller space for non-orientable surfaces, extending understanding of their geometric and dynamical properties.

Contribution

It provides a detailed description of orbit closures in measured lamination and Teichmüller spaces for non-orientable surfaces, including a characterization of closures of weighted two-sided curves.

Findings

Describes possible orbit closures in measured lamination spaces.

Characterizes the closure of weighted two-sided curves.

Provides insights into the dynamics of the mapping class group on 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 $\mathcal M\mathcal L$ and $\mathcal P\mathcal M\mathcal L$ of the mapping class group orbits of measured laminations, projective measured laminations and points in Teichm\"uller space. In particular we obtain a characterization of the closure in $\mathcal M\mathcal L$ of the set of weighted two-sided curves.