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

Yohei Komori; Toshiyuki Sugawa

doi:10.1090/S1088-4173-04-00108-0

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

Yohei Komori, Toshiyuki Sugawa

Research output: Contribution to journal › Article › peer-review

4 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 language	English
Pages (from-to)	115-142
Number of pages	28
Journal	Conformal Geometry and Dynamics
Volume	8
Issue number	5
DOIs	https://doi.org/10.1090/S1088-4173-04-00108-0
Publication status	Published - 2004 Jun 8
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Geometry and Topology

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10.1090/S1088-4173-04-00108-0

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title = "Bers embedding of the teichm{\"U}ller space of a once-punctured torus",

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 Teichm{\"u}ller 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.",

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T1 - Bers embedding of the teichmÜller space of a once-punctured torus

AU - Komori, Yohei

AU - Sugawa, Toshiyuki

PY - 2004/6/8

Y1 - 2004/6/8

N2 - 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.

AB - 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.

KW - Accessory parameter

KW - Bending coordinates

KW - Bers embedding

KW - Monodromy

KW - Once-punctured torus

KW - Pleating ray

KW - Teichmüller space

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

Abstract

Keywords

ASJC Scopus subject areas

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