TY - JOUR
T1 - The teichmüller space of group invariant symmetric structures on the circle
AU - Matsuzaki, Katsuhiko
N1 - Funding Information:
This work was supported by JSPS KAKENHI 25287021.
Publisher Copyright:
© 2017 Annales Academiæ Scientiarum Fennicæ Mathematica.
PY - 2017
Y1 - 2017
N2 - We introduce the quasisymmetric deformation space of a Fuchsian group Γ within the group of symmetric self-homeomorphisms of the circle, and define this as the Teichmüller space AT (Γ) of Γ-invariant symmetric structures. This is another generalization of the asymptotic Teichmüller space, and we verify the basic properties of this space. In particular, we show that AT (Γ) is infinite dimensional, and in fact non-separable if Γ admits a non-trivial deformation, even for a cofinite Fuchsian group Γ.
AB - We introduce the quasisymmetric deformation space of a Fuchsian group Γ within the group of symmetric self-homeomorphisms of the circle, and define this as the Teichmüller space AT (Γ) of Γ-invariant symmetric structures. This is another generalization of the asymptotic Teichmüller space, and we verify the basic properties of this space. In particular, we show that AT (Γ) is infinite dimensional, and in fact non-separable if Γ admits a non-trivial deformation, even for a cofinite Fuchsian group Γ.
KW - Asymptotic Bers embedding
KW - Asymptotic Teichmüller space
KW - Barycentric extension
KW - Complex Banach manifold
KW - Quasiconformal
KW - Quasisymmetric
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U2 - 10.5186/AASFM.2017.4235
DO - 10.5186/AASFM.2017.4235
M3 - Article
AN - SCOPUS:85050995420
SN - 1239-629X
VL - 42
SP - 535
EP - 550
JO - Annales Academiae Scientiarum Fennicae Mathematica
JF - Annales Academiae Scientiarum Fennicae Mathematica
ER -