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}
}
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… 

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