Dynamics of Teichmüller modular groups and topology of moduli spaces of Riemann surfaces of infinite type
type: Item
instance of: scholarly article
title: Dynamics of Teichmüller modular groups and topology of moduli spaces of Riemann surfaces of infinite type
zbMATH Open document ID: 1388.30054
DOI: 10.4171/GGD/437
author: Xianqiang Yang
published in: Groups, Geometry, and Dynamics
publication date: 2018-04-27T00:00:00Z
review text: Summary: We investigate the dynamics of the Teichmüller modular group on the Teichmüller space of a Riemann surface of infinite topological type. Since the modular group does not necessarily act discontinuously, the quotient space cannot inherit a rich geometric structure from the Teichmüller space. However, we introduce the set of points where the action of the Teichmüller modular group is stable, and we prove that this region of stability is generic in the Teichmüller space. By taking the quotient and completion with respect to the Teichmüller distance, we obtain a geometric object that we regard as an appropriate moduli space of the quasiconformally equivalent complex structures admitted on a topologically infinite Riemann surface.
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 37F30
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 6865179
zbMATH Keywords: Riemann surface of infinite type
zbMATH Keywords: Teichmüller modular group
zbMATH Keywords: moduli space
zbMATH Keywords: quasiconformal deformation
zbMATH Keywords: length spectrum
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ggd/437
OpenAlex ID: W2790804859
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description: scientific article; zbMATH DE number 6865179