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

Radnell, David; Schippers, Eric

doi:10.1090/S1088-4173-10-00206-7

Fiber structure and local coordinates for the Teichmüller space of a bordered Riemann surface
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by David Radnell and Eric Schippers

Conform. Geom. Dyn. 14 (2010), 14-34

DOI: https://doi.org/10.1090/S1088-4173-10-00206-7

Published electronically: February 11, 2010

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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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