On laminar groups, Tits alternatives and convergence group actions on 饾憜2
Resumen:
Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups, so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then prove that torsion-free pseudo-fibered groups satisfy a Tits alternative. We conclude by proving that a purely hyperbolic pseudo-fibered group acts on the 2-sphere as a convergence group. This leads to an interesting question if there are examples of pseudo-fibered groups other than 3-manifold groups.
| 2019 | |
| Homeomorphisms of the circle | |
| Ingl茅s | |
| Universidad de la Rep煤blica | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/28485 | |
| Acceso abierto | |
| Licencia Creative Commons Atribuci贸n (CC - By 4.0) |
| Sumario: | Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups, so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then prove that torsion-free pseudo-fibered groups satisfy a Tits alternative. We conclude by proving that a purely hyperbolic pseudo-fibered group acts on the 2-sphere as a convergence group. This leads to an interesting question if there are examples of pseudo-fibered groups other than 3-manifold groups. |
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