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

2009/06/17 by David Radnell, Eric Schippers, Radnell, David +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Geometric and Algebraic Topology #math-ph #math.CV #math.MP #msc:30F60 #msc:58B12 #msc:81T40

paper · pdf · doi:10.48550/arxiv.0906.3279

21 pages

arxiv created 2009/06/17 · arxiv updated 2009/12/01

Abstract

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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