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

Yohei Komori, Toshiyuki Sugawa

Research output: Contribution to journalArticle

2 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
Pages (from-to)115-142
Number of pages28
JournalConformal Geometry and Dynamics
Volume8
Issue number5
DOIs
Publication statusPublished - 2004 Jun 8
Externally publishedYes

Fingerprint

Torus
Heun Equation
Projective Structure
Differential equation
Fuchsian Group
Generator
Computing

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Bers embedding of the teichmÜller space of a once-punctured torus. / Komori, Yohei; Sugawa, Toshiyuki.

In: Conformal Geometry and Dynamics, Vol. 8, No. 5, 08.06.2004, p. 115-142.

Research output: Contribution to journalArticle

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