The teichmüller space of group invariant symmetric structures on the circle

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    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.

    元の言語English
    ページ(範囲)535-550
    ページ数16
    ジャーナルAnnales Academiae Scientiarum Fennicae Mathematica
    42
    DOI
    出版物ステータスPublished - 2017 1 1

    ASJC Scopus subject areas

    • Mathematics(all)

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