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Examples of pleating varieties for twice punctured tori

Authors: Raquel Díaz and Caroline Series
Journal: Trans. Amer. Math. Soc. 356 (2004), 621-658
MSC (2000): Primary 30F40, 20H10, 32G15
Published electronically: September 22, 2003
MathSciNet review: 2022714
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Abstract: We give an explicit description of some pleating varieties (sets with a fixed set of bending lines in the convex hull boundary) in the quasi-Fuchsian space of the twice punctured torus. In accordance with a conjecture of the second author, we show that their closures intersect Fuchsian space in the simplices of minima introduced by Kerckhoff. All computations are done using complex Fenchel-Nielsen coordinates for quasi-Fuchsian space referred to a maximal system of curves.

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Additional Information

Raquel Díaz
Affiliation: Departamento de Geometría y Topología, Facultad Matemáticas, Universidad Complutense, 28040 Madrid, Spain

Caroline Series
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

Received by editor(s): August 21, 2001
Received by editor(s) in revised form: July 11, 2002
Published electronically: September 22, 2003
Article copyright: © Copyright 2003 American Mathematical Society