Complex Fenchel-Nielsen coordinates with small imaginary parts
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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.References
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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
- 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.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3267018