Conjugacy classes of big mapping class groups

Jesús Hernández Hernández; Michael Hrušák; Israel Morales; Anja Randecker; Manuel Sedano; Ferrán Valdez

Conjugacy classes of big mapping class groups

Geometric Topology 2021-11-22 v3 Dynamical Systems Logic

Authors: Jesús Hernández Hernández , Michael Hrušák , Israel Morales , Anja Randecker , Manuel Sedano , Ferrán Valdez

Abstract

We describe the topological behavior of the conjugacy action of the mapping class group of an orientable infinite-type surface $\Sigma$ on itself. Our main results are: (1) All conjugacy classes of $MCG(\Sigma)$ are meager for every $\Sigma$ , (2) $MCG(\Sigma)$ has a somewhere dense conjugacy class if and only if $\Sigma$ has at most two maximal ends and no non-displaceable finite-type subsurfaces, (3) $MCG(\Sigma)$ has a dense conjugacy class if and only if $\Sigma$ has a unique maximal end and no non-displaceable finite-type subsurfaces. Our techniques are based on model-theoretic methods developed by Kechris, Rosendal and Truss.

Keywords

conjugacy classes in groups mapping class groups of surfaces mapping class groups

Cite

@article{arxiv.2105.11282,
  title  = {Conjugacy classes of big mapping class groups},
  author = {Jesús Hernández Hernández and Michael Hrušák and Israel Morales and Anja Randecker and Manuel Sedano and Ferrán Valdez},
  journal= {arXiv preprint arXiv:2105.11282},
  year   = {2021}
}

Comments

v3. Corrected version after revision. To appear in J. London Math. Soc

Conjugacy classes of big mapping class groups

Abstract

Keywords

Cite

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