TY - JOUR
T1 - Dynamics of teichmüller modular groups and topology of moduli spaces of Riemann surfaces of infinite type
AU - Matsuzaki, Katsuhiko
N1 - Publisher Copyright:
© European Mathematical Society.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Hyperbolic geometry
KW - Length spectrum
KW - Limit set
KW - Moduli space
KW - Quasiconformal deformation
KW - Region of discontinuity
KW - Riemann surface of infinite type
KW - Teichmüller modular group
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U2 - 10.4171/GGD/437
DO - 10.4171/GGD/437
M3 - Article
AN - SCOPUS:85045926089
VL - 12
SP - 1
EP - 64
JO - Groups, Geometry, and Dynamics
JF - Groups, Geometry, and Dynamics
SN - 1661-7207
IS - 1
ER -