Fiber Structure and Local Coordinates for the Teichmueller Space of a Bordered Riemann Surface

Details Fiber Structure and Local Coordinates for the Teichmueller Space of a Bordered Riemann Surface Fiber Structure and Local Coordinates for the Teichmueller Space of a Bordered Riemann Surface

2009-06-17

arxiv.org/abs/0906.3279v1

Mathematics

Complex Variables

21 pages

Scientific paper

We show that the infinite-dimensional Teichmueller space of a Riemann surface whose boundary consists of n closed curves is a holomorphic fiber space over the Teichmueller space of n-punctured surfaces. Each fiber is a complex Banach manifold modeled on a two-dimensional extension of the universal Teichmueller space. The local model of the fiber, together with the coordinates from internal Schiffer variation, provides new holomorphic local coordinates for the infinite-dimensional Teichmueller space.

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