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

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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.
Publisher
WALTER DE GRUYTER GMBH
Issue Date
2019-05
Language
English
Article Type
Article
Citation

JOURNAL OF GROUP THEORY, v.22, no.3, pp.359 - 381

ISSN
1433-5883
DOI
10.1515/jgth-2019-2047
URI
http://hdl.handle.net/10203/261862
Appears in Collection
MA-Journal Papers(저널논문)
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