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Transactions of the American Mathematical Society

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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
Published electronically: September 4, 2014
MathSciNet review: 3267018
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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.

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Dragomir Šarić
Affiliation: Department of Mathematics, Queens College of CUNY, 65-30 Kissena Boulevard, Flushing, New York 11367

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.

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