Geodesic
Dynamics of Teichmüller modular groups and topology of moduli spaces of Riemann surfaces of infinite type
Katsuhiko Matsuzaki1 orcid
1Waseda University, Tokyo, Japan
Groups, geometry, and dynamics, Tome 12 (2018) no. 1, pp. 1-64

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DOI

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.
DOI : 10.4171/ggd/437
Classification : 30-XX, 32-XX, 37-XX
Mots-clés : Teichmüller modular group, moduli space, Riemann surface of infinite type, quasiconformal deformation, hyperbolic geometry, length spectrum, limit set, region of discontinuity

Katsuhiko Matsuzaki  1

1 Waseda University, Tokyo, Japan 
Katsuhiko Matsuzaki. Dynamics of Teichmüller modular groups and topology of moduli spaces of Riemann surfaces of infinite type. Groups, geometry, and dynamics, Tome 12 (2018) no. 1, pp. 1-64. doi: 10.4171/ggd/437
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     title = {Dynamics of {Teichm\"uller} modular groups and topology of moduli spaces of {Riemann} surfaces of infinite type},
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     year = {2018},
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