Drawing bers embeddings of the teichmüller space of once-punctured tori

Yohei Komori, Toshiyuki Sugawa, Masaaki Wada, Yasushi Yamashita

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We present a computer-oriented method of producing pictures of Bers embeddings of the Teichmüller space of once-punctured tori. The coordinate plane is chosen in such a way that the accessory parameter is hidden in the relative position of the origin. Our algorithm consists of two steps. For each point in the coordinate plane, we first compute the corresponding monodromy representation by numerical integration along certain loops. Then we decide whether the representation is discrete by applying Jørgensen's theory on the quasi-Fuchsian space of once-punctured tori.

Original languageEnglish
Pages (from-to)51-60
Number of pages10
JournalExperimental Mathematics
Volume15
Issue number1
Publication statusPublished - 2006
Externally publishedYes

Fingerprint

Cartesian plane
Torus
Monodromy
Numerical integration
Drawing

Keywords

  • Bers embedding
  • Kleinian groups
  • Teichmüller space

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Drawing bers embeddings of the teichmüller space of once-punctured tori. / Komori, Yohei; Sugawa, Toshiyuki; Wada, Masaaki; Yamashita, Yasushi.

In: Experimental Mathematics, Vol. 15, No. 1, 2006, p. 51-60.

Research output: Contribution to journalArticle

Komori, Y, Sugawa, T, Wada, M & Yamashita, Y 2006, 'Drawing bers embeddings of the teichmüller space of once-punctured tori', Experimental Mathematics, vol. 15, no. 1, pp. 51-60.
Komori, Yohei ; Sugawa, Toshiyuki ; Wada, Masaaki ; Yamashita, Yasushi. / Drawing bers embeddings of the teichmüller space of once-punctured tori. In: Experimental Mathematics. 2006 ; Vol. 15, No. 1. pp. 51-60.
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