The teichmüller space of group invariant symmetric structures on the circle

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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 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

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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