Surface groups of diffeomorphisms of the interval. (English) Zbl 1443.20062
Summary: We prove that the group of diffeomorphisms of the interval \([0, 1]\) contains surface groups whose action on \((0, 1)\) has no global fix point and such that only countably many points of the interval \((0, 1)\) have non-trivial stabiliser.
MSC:
| 20F34 | Fundamental groups and their automorphisms (group-theoretic aspects) |
| 37C05 | Dynamical systems involving smooth mappings and diffeomorphisms |
| 37C85 | Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) |
| 37E05 | Dynamical systems involving maps of the interval |
| 57M60 | Group actions on manifolds and cell complexes in low dimensions |
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