Bers embedding of the Teichmüller space of a once-punctured torus

Yohei Komori, Toshiyuki Sugawa

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this note, we present a method of computing monodromies of projective structures on a once-punctured torus. This leads to an algorithm numerically visualizing the shape of the Bers embedding of a one-dimensional Teichmüller space. As a by-product, the value of the accessory parameter of a four-times punctured sphere will be calculated in a numerical way as well as the generators of a Fuchsian group uniformizing it. Finally, we observe the relation between the Schwarzian differential equation and Heun's differential equation in this special case.

Original languageEnglish
JournalConformal Geometry and Dynamics
Volume8
Publication statusPublished - 2004 Dec 1

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Keywords

  • Accessory parameter
  • Bending coordinates
  • Bers embedding
  • Monodromy
  • Once-punctured torus
  • Pleating ray
  • Teichmueller space
  • Teichmuller space

ASJC Scopus subject areas

  • Geometry and Topology

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