Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 535-550

THE TEICHMÜLLER SPACE OF GROUP INVARIANT SYMMETRIC STRUCTURES ON THE CIRCLE

Katsuhiko Matsuzaki

Waseda University, School of Education, Department of Mathematics
Shinjuku, Tokyo 169-8050, Japan; matsuzak 'at' waseda.jp

Abstract. 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.

2010 Mathematics Subject Classification: Primary 30F60; Secondary 32G15.

Key words: Quasiconformal, quasisymmetric, asymptotic Teichmüuller space, asymptotic Bers embedding, barycentric extension, complex Banach manifold.

Reference to this article: K. Matsuzaki: The Teichmüller space of group invariant symmetric structures on the circle. Ann. Acad. Sci. Fenn. Math. 42 (2017), 535-550.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4235