Fuchsian groups, circularly ordered groups and dense invariant laminations on the circle

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We propose a program to study groups acting faithfully on S-1 in terms of numbers of pairwise transverse dense invariant laminations. We give some examples of groups that admit a small number of invariant laminations as an introduction to such groups. The main focus of the present paper is to characterize Fuchsian groups in this scheme. We prove a group acting on S-1 is conjugate to a Fuchsian group if and only if it admits three very full laminations with a variation on the transversality condition. Some partial results toward a similar characterization of hyperbolic 3-manifold groups that fiber over the circle have been obtained. This work was motivated by the universal circle theory for tautly foliated 3-manifolds developed by Thurston, Calegari and Dunfield.
Publisher
GEOMETRY & TOPOLOGY PUBLICATIONS
Issue Date
2015-07
Language
English
Article Type
Article
Citation

GEOMETRY & TOPOLOGY, v.19, no.4, pp.2081 - 2115

ISSN
1465-3060
DOI
10.2140/gt.2015.19.2081
URI
http://hdl.handle.net/10203/221026
Appears in Collection
MA-Journal Papers(저널논문)
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