Experimental Mathematics

Drawing Bers Embeddings of the Teichmüller Space of Once-Punctured Tori

Yohei Komori, Toshiyuki Sugawa, Masaaki Wada, and Yasushi Yamashita

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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.

Article information

Source
Experiment. Math. Volume 15, Number 1 (2006), 51-60.

Dates
First available in Project Euclid: 16 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.em/1150476903

Mathematical Reviews number (MathSciNet)
MR2229385

Zentralblatt MATH identifier
1106.30027

Subjects
Primary: 30F60: Teichmüller theory [See also 32G15] 30F40: Kleinian groups [See also 20H10] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]

Keywords
Bers embedding Teichmüller space Kleinian groups

Citation

Komori, Yohei; Sugawa, Toshiyuki; Wada, Masaaki; Yamashita, Yasushi. Drawing Bers Embeddings of the Teichmüller Space of Once-Punctured Tori. Experiment. Math. 15 (2006), no. 1, 51--60. https://projecteuclid.org/euclid.em/1150476903.


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