### Mapping class group orbit closures for non-orientable surfaces

Ergodic Theory and Dynamical Systems Seminar

6th June 2024, 2:00 pm – 3:00 pm

Fry Building, G.07

The space of measured laminations on a hyperbolic surface is a generalisation of the set of weighted multi curves. The action of the mapping class group on this space is an important tool in the study of the geometry of the surface.

For orientable surfaces, orbit closures are now well-understood and were classified by Lindenstrauss and Mirzakhani. In particular, it is one of the pillars of Mirzakhani’s curve counting theorems.

For non-orientable surfaces, the behaviour of this action is very different and the classification fails. In this talk I will review some of these differences and talk about how to describe mapping class group orbit closures of (projective) measured laminations for non-orientable surfaces. This is joint work with Erlandsson, Gendulphe and Souto.

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