Conjugacy classes of big mapping class groups

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

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arXiv · 2105.11282

Conjugacy classes of big mapping class groups

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

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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.

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BibTeX RIS

Jesús Hernández Hernández, Michael Hrušák, Israel Morales, Anja Randecker, Manuel Sedano, Ferrán Valdez. 2021-05-24. Conjugacy classes of big mapping class groups. https://arxiv.org/abs/2105.11282

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