Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

Complex Fenchel-Nielsen coordinates with small imaginary parts


Author: Dragomir Šarić
Journal: Trans. Amer. Math. Soc. 366 (2014), 6541-6565
MSC (2010): Primary 30F40, 32G15
DOI: https://doi.org/10.1090/S0002-9947-2014-06101-1
Published electronically: September 4, 2014
MathSciNet review: 3267018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Kahn and Markovic (2012) proved that the fundamental group of each closed hyperbolic three manifold contains a closed surface subgroup. One of the main ingredients in their proof is a theorem which states that an assignment of nearly real, complex Fenchel-Nielsen coordinates to the cuffs of a pants decomposition of a closed surface $ S$ induces a quasi-Fuchsian representation of the fundamental group of $ S$. We give a new proof of this theorem with slightly stronger conditions on the Fenchel-Nielsen coordinates and explain how to use the exponential mixing of the geodesic flow on a closed hyperbolic three manifold to prove that our theorem is sufficient for the applications in the work of Kahn and Markovic.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 30F40, 32G15

Retrieve articles in all journals with MSC (2010): 30F40, 32G15


Additional Information

Dragomir Šarić
Affiliation: Department of Mathematics, Queens College of CUNY, 65-30 Kissena Boulevard, Flushing, New York 11367
Email: Dragomir.Saric@qc.cuny.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06101-1
Received by editor(s): April 25, 2012
Received by editor(s) in revised form: February 2, 2013
Published electronically: September 4, 2014
Additional Notes: This research was partially supported by National Science Foundation grant DMS 1102440.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.