Virtual critical regularity of mapping class group actions on the circle. (English) Zbl 07928076
Summary: We show that if \(G_1\) and \(G_2\) are non-solvable groups, then no \(C^{1, \tau}\) action of \((G_1\times G_2)*\mathbb{Z}\) on \(S^1\) is faithful for \(\tau > 0\). As a corollary, if \(S\) is an orientable surface of complexity at least three then the critical regularity of an arbitrary finite index subgroup of the mapping class group \(\operatorname{Mod}(S)\) with respect to the circle is at most one, thus strengthening a result of the first two authors with Baik.
MSC:
| 57M60 | Group actions on manifolds and cell complexes in low dimensions |
| 20F36 | Braid groups; Artin groups |
| 37C05 | Dynamical systems involving smooth mappings and diffeomorphisms |
| 37C85 | Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) |
| 20F14 | Derived series, central series, and generalizations for groups |
| 20F60 | Ordered groups (group-theoretic aspects) |
Keywords:
free group; non-solvable group; smoothing; critical regularity; mapping class group; invariant measureReferences:
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