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ON STABILIZERS OF SOME TEICHMÜLLER DISKS IN POINTED MAPPING CLASS GROUPS

Published online by Cambridge University Press:  25 August 2010

C. ZHANG
C. ZHANG*
Affiliation:
Department of Mathematical Sciences, Morehouse College, Atlanta, GA 30314, USA e-mail: [email protected]
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Abstract

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We prove that for each Riemann surface of finite analytic type (p, n) with p ≥ 2, there exist uncountably many Teichmüller disks Δ in the Teichmüller space T(S), where S = - {a point a}, with these properties: (1) the natural projection j: T(S) → T() defined by forgetting a induces an isometric embedding of each Δ into T(); and (2) the stabilizer of each Teichmüller disk Δ in the a-pointed mapping class group of S is trivial.

Keywords

30C6030F60
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 593 - 604
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Abikoff, W., The real analytic theory of Teichmüller spaces, Lecture notes in mathematics 820 (Springer-Verlag, Berlin–New York, 1980).Google Scholar
2.Ahlfors, L. V. and Bers, L., Riemann's mapping theorem for variable metrics, Ann. Math. 72 (2) (1960), 385–404.CrossRefGoogle Scholar
3.Arnoux, P. and Yoccoz, J. C., Construction de diffeomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sr. I Math. 292 (1) (1981), 75–78.Google Scholar
4.Beardon, A., The geometry of discrete groups (Springer-Verlag, New York, 1983).CrossRefGoogle Scholar
5.Bers, L., Fiber spaces over Teichmüller spaces, Acta Math. 130 (1973), 89–126.CrossRefGoogle Scholar
6.Bers, L., An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), 73–98.Google Scholar
7.Earle, C. J. and Gardiner, F., Teichmüller disks and Veech's -structures, Contemp. Math. 201 (1997), 165–189.Google Scholar
8.Hubert, P. and Lanneau, E., Veech group without parabolic elements, Duke Math. J. 133 (2006), 335–346.CrossRefGoogle Scholar
9.Farkas, H. M. and Kra, I., Riemann surfaces (Springer-Verlag, New York, 1980).CrossRefGoogle Scholar
10.Kerckhoff, S. P., The Nielsen realisation problem, Ann. Math. 117 (1983), 235–265.CrossRefGoogle Scholar
11.Kra, I., On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), 231–270.CrossRefGoogle Scholar
12.Kravetz, S., On the geometry of Teichmüller spaces and the structure of their modular groups, Ann. Acad. Sci. Fenn. Math. 278 (1959), 135.Google Scholar
13.Kenyon, R. and Smillie, J., Billiards in rational-angled triangles, Comment. Math, Helv. 75 (2000), 65–108.Google Scholar
14.Purzitsky, N., A cutting and pasting of noncompact polygons with applications to Fuchsian groups, Acta Math. 143 (1979), 233–250.Google Scholar
15.Strebel, K., Quadratic differentials (Springer-Verlag, Berlin, 1984).Google Scholar
16.Thurston, W. P., On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. (N.S.) 19 (1988), 417–431.CrossRefGoogle Scholar
17.Veech, W. A., Teichmüller curves in moduli space, Einstein series and an application to triangular billiards. Invent. Math. 97 (1989), 553–583.CrossRefGoogle Scholar