Examples of pleating varieties for twice punctured tori

Díaz, Raquel; Series, Caroline

doi:10.1090/S0002-9947-03-03179-9

Examples of pleating varieties for twice punctured tori
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by Raquel Díaz and Caroline Series PDF

Trans. Amer. Math. Soc. 356 (2004), 621-658 Request permission

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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