The teichmüller space of group invariant symmetric structures on the circle

    Research output: Contribution to journalArticle

    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.

    Original languageEnglish
    Pages (from-to)535-550
    Number of pages16
    JournalAnnales Academiae Scientiarum Fennicae Mathematica
    Volume42
    DOIs
    Publication statusPublished - 2017 Jan 1

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    Circle
    Fuchsian Group
    Invariant
    Nonseparable
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    Keywords

    • Asymptotic Bers embedding
    • Asymptotic Teichmüller space
    • Barycentric extension
    • Complex Banach manifold
    • Quasiconformal
    • Quasisymmetric

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

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    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 Teichm{\"u}ller space AT (Γ) of Γ-invariant symmetric structures. This is another generalization of the asymptotic Teichm{\"u}ller 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.",
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