On laminar groups, Tits alternatives and convergence group actions on 𝑆2-Reference-Cited by-同舟云学术

On laminar groups, Tits alternatives and convergence group actions on 𝑆2

Published:2019-03-21 Issue:3 Volume:22 Page:359-381
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Alonso Juan¹,Baik Hyungryul²,Samperton Eric³

Affiliation:

1. Centro de Matemática , Facultad de Ciencias , Universidad de la República , Iguá 4225 , Montevideo C.P. 11400 , Uruguay

2. Department of Mathematical Sciences , KAIST , 291 Daehak-ro Yuseong-gu , Daejeon , 34141 , South Korea

3. Department of Mathematics , South Hall, Room 6607 , University of California , Santa Barbara , CA 93106-3080 , USA

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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