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

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.

15 pages, 5 figures. A minor revision has been done based on the referee's comments. To appear in Journal of Group Theory

References in corpus (3)

• Spaces of invariant circular orders of groups
• Fuchsian Groups, Circularly Ordered Groups, and Dense Invariant Laminations on the Circle
• Quasigeodesic flows and sphere-filling curves