Laminations On The Circle And Hyperbolic Geometry
Loading...
Files
No Access Until
Permanent Link(s)
Collections
Other Titles
Author(s)
Abstract
We develop a program studying group actions on the circle with dense invariant laminations. Such actions naturally and frequently arise in the study of hyperbolic manifolds. We use the convergence group theorem to prove that for a discrete torsion-free group acting on the circle, it is topologically conjugate to a ยจ Mobius group if and only if it admits three very-full invariant laminations with a certain transversality condition. We also discuss the case when a group acts on the circle with two very-full invariant laminations with disjoint endpoints. We show that such a group shares many interesting features with the fundamental group of a hyperbolic 3-manifold which fibers over the circle.
Journal / Series
Volume & Issue
Description
Sponsorship
Date Issued
2014-08-18
Publisher
Keywords
Lamination; Hyperbolic Geometry; Fuchsian Group
Location
Effective Date
Expiration Date
Sector
Employer
Union
Union Local
NAICS
Number of Workers
Committee Chair
Hubbard, John Hamal
Committee Co-Chair
Committee Member
Smillie, John D
Hatcher, Allen E
Thurston, Dylan P.
Hass, Joel
Hatcher, Allen E
Thurston, Dylan P.
Hass, Joel
Degree Discipline
Mathematics
Degree Name
Ph. D., Mathematics
Degree Level
Doctor of Philosophy
Related Version
Related DOI
Related To
Related Part
Based on Related Item
Has Other Format(s)
Part of Related Item
Related To
Related Publication(s)
Link(s) to Related Publication(s)
References
Link(s) to Reference(s)
Previously Published As
Government Document
ISBN
ISMN
ISSN
Other Identifiers
Rights
Rights URI
Types
dissertation or thesis