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Conformal Geometry and Dynamics

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Fiber structure and local coordinates for the Teichmüller space of a bordered Riemann surface

Authors: David Radnell and Eric Schippers
Journal: Conform. Geom. Dyn. 14 (2010), 14-34
MSC (2010): Primary 30F60, 58B12; Secondary 81T40
Published electronically: February 11, 2010
MathSciNet review: 2593332
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Abstract: We show that the infinite-dimensional Teichmüller space of a Riemann surface whose boundary consists of $ n$ closed curves is a holomorphic fiber space over the Teichmüller space of an $ n$-punctured surface. Each fiber is a complex Banach manifold modeled on a two-dimensional extension of the universal Teichmüller space. The local model of the fiber, together with the coordinates from internal Schiffer variation, provides new holomorphic local coordinates for the infinite-dimensional Teichmüller space.

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Additional Information

David Radnell
Affiliation: Department of Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates

Eric Schippers
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

Keywords: Teichm\"uller spaces, quasiconformal mappings, sewing, rigged Riemann surfaces, conformal field theory
Received by editor(s): June 17, 2009
Published electronically: February 11, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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