Mapping class groups with the Rokhlin property

TL;DR

This paper investigates the properties of mapping class groups of connected orientable 2-manifolds, focusing on the existence of dense and comeager conjugacy classes, and provides a classification based on these properties.

Contribution

The paper classifies which connected orientable 2-manifolds have mapping class groups with dense conjugacy classes and characterizes when these groups have comeager conjugacy classes.

Findings

Mapping class groups of certain 2-manifolds have dense conjugacy classes.

A mapping class group has a comeager conjugacy class if and only if it is trivial.

The classification links the topological properties of the manifold to algebraic properties of its mapping class group.

Abstract

We classify the connected orientable 2-manifolds whose mapping class groups have a dense conjugacy class. We also show that the mapping class group of a connected orientable 2-manifold has a comeager conjugacy class if and only if the mapping class group is trivial.