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Earle slices associated with involutions for once punctured torus. (English) Zbl 1311.30021

Summary: In this paper, we will study Earle slices of quasi-fuchsian space for once punctured torus associated with involutions of its fundamental group induced by orientation reversing diffeomorphism of this surface. First we classify Earle slices into two types: rhombic Earle slices and rectangular Earle slices. The main purpose of this paper is to study the configuration of Earle slices. Especially, we obtain a necessary and sufficient condition for two Earle slices to intersect each other. We also show that the union of all Earle slices is connected. In the end, we describe Earle slices by using trace coordinates of quasi-fuchsian space.

MSC:

30F60 Teichmüller theory for Riemann surfaces
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
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References:

[1] B. H. Bowditch, Markoff triples and quasi-Fuchsian groups, Proc. London Math. Soc. (3) 77 (1998), no. 3, 697-736. · Zbl 0928.11030
[2] C. J. Earle, Some intrinsic coordinates on Teichmller space, Proc. Amer. Math. Soc. 83 (1981), no. 3, 527-531. · Zbl 0478.32015
[3] B. Farb and D. Margalit, A primer on mapping class groups , Princeton Mathematical Series 49, Princeton University Press, Princeton, NJ, 2012. · Zbl 1245.57002
[4] D. E. Flath, Introduction to Number Theory , New York, Wiley, 1989. · Zbl 0651.10001
[5] L. Keen, Teichmller spaces of punctured tori: I, II , Complex Variables, Theory and Appl. 2 (1983), no. 2, 199-211, 213-225. · Zbl 0503.30036
[6] Y. Komori, C. Series, Pleating coordinates for the Earle embedding, Ann. Fac. Sci. Toulouse Math. (6) 10 (2001), no. 1, 69-105. · Zbl 1004.30031
[7] Y. Komori, A note on a paper of T. Sasaki, Proceedings of the Second ISAAC Congress, Vol. 2 (Fukuoka, 1999), 11091115, Int. Soc. Anal. Appl. Comput., 8, Kluwer Acad. Publ., Dordrecht, 2000.
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