By Lvzhou Chen
Appears in collection : 2024 - T2 - WS1 - Low Dimensional Actions
Surfaces of infinite type, such as the plane minus a Cantor set, occur naturally in dynamics. However, their mapping class groups are much less understood compared to the mapping class groups of surfaces of finite type. For the mapping class group G of the plane minus a Cantor set, we show that any nontrivial G-action on the circle is semi-conjugate to its action on the so-called simple circle. I will also explain what happens in the more general situation where we replace the plane by a once-punctured surface of finite genus. This is mostly based on joint work with Danny Calegari.
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