# Conjugacy classes of big mapping class groups

@article{HernndezHernndez2021ConjugacyCO,
title={Conjugacy classes of big mapping class groups},
author={Jes{\'u}s Hern{\'a}ndez Hern{\'a}ndez and Michael Hrus{\'a}k and Israel Morales and Anja Randecker and Manuel Sedano and Ferr{\'a}n Valdez},
journal={Journal of the London Mathematical Society},
year={2021},
volume={106}
}
• Published 24 May 2021
• Mathematics
• Journal of the London Mathematical Society
We describe the topological behavior of the conjugacy action of the mapping class group of an orientable infinite‐type surface Σ$\Sigma$ on itself by proving that: (1)all conjugacy classes of Map(Σ)$\operatorname{Map}(\Sigma )$ are meager for every Σ$\Sigma$ , (2) Map(Σ)$\operatorname{Map}(\Sigma )$ has a somewhere dense conjugacy class if and only if Σ$\Sigma$ has at most two maximal ends and no non‐displaceable finite‐type subsurfaces, (3) Map(Σ)$\operatorname{Map}(\Sigma )$ has a dense…
1 Citations

### Mapping class groups with the Rokhlin property

• Mathematics
Mathematische Zeitschrift
• 2022
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

## References

SHOWING 1-10 OF 20 REFERENCES

### Algebraic and topological properties of big mapping class groups

• Mathematics
Algebraic & Geometric Topology
• 2018
Let $S$ be an orientable, connected surface with infinitely-generated fundamental group. The main theorem states that if the genus of $S$ is finite and at least 4, then the isomorphism type of the

### A primer on mapping class groups

• Mathematics
• 2013
Given a compact connected orientable surface S there are two fundamental objects attached: a group and a space. The group is the mapping class group of S, denoted by Mod(S). This group is defined by

### Turbulence, amalgamation, and generic automorphisms of homogeneous structures

• Mathematics
• 2004
We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy

### Large scale geometry of big mapping class groups

• Mathematics
• 2019
We study the large-scale geometry of mapping class groups of surfaces of infinite type, using the framework of Rosendal for coarse geometry of non locally compact groups. We give a complete

### Isomorphisms between curve graphs of infinite-type surfaces are geometric

• Mathematics
Rocky Mountain Journal of Mathematics
• 2018
Let $\phi:\mathcal{C}(S)\to\mathcal{C}(S')$ be a simplicial isomorphism between the curve graphs of two infinite-type surfaces. In this paper we show that in this situation $S$ and $S'$ are

### The First Integral Cohomology of Pure Mapping Class Groups

• Mathematics
• 2017
It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we construct nontrivial

### Automatic continuity for homeomorphism groups of noncompact manifolds

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that,

### The end point compactification of manifolds.

Introduction^ This paper originated in trying to show that the one point compactification of an orientable generalized ^-manifold (n-grn) with cohomology isomorphic to Euclidean n-space was an

### london mathematical society lecture note series

• Mathematics
• 2007
Denis Benois. Trivial zeros of p-adic L-functions and Iwasawa theory. We prove that the expected properties of Euler systems imply quite general MazurTate-Teitelbaum type formulas for derivatives of