On laminar groups, Tits alternatives, and convergence group actions on $S^2$

Juan Alonso; Hyungryul Baik; Eric Samperton

doi:10.1515/jgth-2019-2047

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arXiv · 1411.3532

On laminar groups, Tits alternatives, and convergence group actions on $S^2$

Juan Alonso·Hyungryul Baik·Eric Samperton

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Abstract

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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Juan Alonso, Hyungryul Baik, Eric Samperton. 2014-11-13. On laminar groups, Tits alternatives, and convergence group actions on $S^2$. https://doi.org/10.1515/jgth-2019-2047

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