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Conformal Geometry and Dynamics

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Conformal grafting and convergence of Fenchel-Nielsen twist coordinates

Author: Maxime Fortier Bourque
Journal: Conform. Geom. Dyn. 19 (2015), 1-18
MSC (2010): Primary 30F60; Secondary 30F45
Published electronically: January 23, 2015
MathSciNet review: 3302905
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Abstract: We cut a hyperbolic surface of finite area along some analytic simple closed curves, and glue in cylinders of varying moduli. We prove that as the moduli of the glued cylinders go to infinity, the Fenchel-Nielsen twist coordinates for the resulting surface around those cylinders converge.

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Additional Information

Maxime Fortier Bourque
Affiliation: Department of Mathematics, The Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016

Keywords: Teichm\"uller space, Fenchel-Nielsen coordinates, hyperbolic metric, geometric convergence, distortion theorem
Received by editor(s): September 10, 2014
Published electronically: January 23, 2015
Additional Notes: The author’s research was partially supported by the Natural Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 2015 American Mathematical Society