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Coherence of Limit Points in the Fibers over the Asymptotic Teichmüller Space

Coherence of Limit Points in the Fibers over the Asymptotic Teichmüller Space We consider the infinite dimensional Teichmüller space of a Riemann surface of general type. On the basis of the fact that the action of the quasiconformal mapping class group on the Teichmüller space is not discontinuous, in general, we divide the Teichmüller space into two disjoint subsets, the limit set and the region of discontinuity, according to the discreteness of the orbit by a subgroup of the quasiconformal mapping class group. The asymptotic Teichmüller space is a certain quotient space of the Teichmüller space and there is a natural projection from the Teichmüller space to the asymptotic Teichmüller space. We consider the fibers of the projection over any point in the asymptotic Teichmüller space, and show a coherence of the discreteness on each fiber in the Teichmüller space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Coherence of Limit Points in the Fibers over the Asymptotic Teichmüller Space

Computational Methods and Function Theory , Volume 14 (3) – Apr 29, 2014

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0066-y
Publisher site
See Article on Publisher Site

Abstract

We consider the infinite dimensional Teichmüller space of a Riemann surface of general type. On the basis of the fact that the action of the quasiconformal mapping class group on the Teichmüller space is not discontinuous, in general, we divide the Teichmüller space into two disjoint subsets, the limit set and the region of discontinuity, according to the discreteness of the orbit by a subgroup of the quasiconformal mapping class group. The asymptotic Teichmüller space is a certain quotient space of the Teichmüller space and there is a natural projection from the Teichmüller space to the asymptotic Teichmüller space. We consider the fibers of the projection over any point in the asymptotic Teichmüller space, and show a coherence of the discreteness on each fiber in the Teichmüller space.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Apr 29, 2014

References