2012/04/25 by Dragomir Šarić, Šarić, Dragomir · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.GT
paper · pdf · doi:10.48550/arxiv.1204.5778
25 pages, 6 figures
arxiv created 2012/04/25 · openalex publication_date 2012/04/25 · arxiv updated 2012/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kahn and Markovic \citeKahnMark 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 quasiFuchsian representation of the fundamental group of S. We give a new proof of this theorem with a 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 \citeKahnMark.