Big mapping class groups and rigidity of the simple circle

Abstract

Let $\Gamma$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $\Gamma$ on the circle is either trivial or semi-conjugate to a unique minimal action on the so-called simple circle.

v4: fixed a typo in the proof of Theorem 5.4

References in corpus (5)

• Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group
• Hyperbolicité du graphe des rayons et quasi-morphismes sur un gros groupe modulaire
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Cited by in corpus (3)

• Nielsen realization for infinite-type surfaces
• Braided Thompson groups with and without quasimorphisms
• On the homology of big mapping class groups