1. On laminar groups, Tits alternatives and convergence group actions on 2
- Author
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Hyungryul Baik, Eric Samperton, Juan Alonso, Alonso Juan, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática., Baik H., and Samperton E.
- Subjects
20F65, 20H10, 37C85, 37E10, 57M60 ,Algebra and Number Theory ,010102 general mathematics ,Geometric Topology (math.GT) ,Laminar flow ,Group Theory (math.GR) ,01 natural sciences ,Homeomorphisms of the circle ,Mathematics - Geometric Topology ,Group action ,0103 physical sciences ,FOS: Mathematics ,Applied mathematics ,010307 mathematical physics ,Convergence (relationship) ,0101 mathematics ,Mathematics - Group Theory ,Mathematics - 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
- Published
- 2019