Fixed points parameters for Teichmüller space of closed Riemann surfaces
DOI:
https://doi.org/10.22199/S0716-09172000000100006Keywords:
Kleinian groups, Teichmüller space, grupos kleinianos, espacio de Teichmüller.Abstract
In this note we provide a set of parameters for the Teichmüller space, of genus g ? 2, given by fixed points of some special set of generators for the uniformizing Fuchsian groups. Explicit computations are given in low genus.
References
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[5] R.A. Hidalgo. “Fixed point parameters for Fuchsian groups of type (1; 2; 0)”. Accepted for publication in Revista Scientia.
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[13] B. Maskit. “Parameters for Fuchsian groups I: Signature (0,4)”. Holomorphic Functions and Moduli II, pp. 251–265. Math. Sci. Res. Inst. Pub. 11. Springer - Verlag, New York, (1988).
[14] B. Maskit. “Parameters for Fuchsian groups II: topological type (1,1)”. Annal. Acad. Sci. Fenn. Ser. A.I. 14, pp. 265–275, (1990).
[15] B. Maskit. “Explicit Matrices for Fuchsian groups”. Preprint IHES/M/92/6 Février (1992).
[16] B. Maskit. Kleinian Groups. Grundlehren der Mathematischen Wissenschaften, vol. 287,Springer - Verlag, Berlin, Heildelberg, New York, (1988).
[17] C. Min. “New parameters of Teichmüller spaces of Riemann surfaces of genus two”. Ann. Acad. Scie. Fenn., Series A.I. Mathematica, Vol.17, (1992).
[18] S. Nag. The complex analytic theory of Teichmüller spaces. Canadian Mathematical Society Series of Monographs and Advances texts. AWiley Interscience Pub. (1988).
[19] M. Seppala and T. Sorvali. “On geometric parametrization of Teichmüller spaces”. Ann. Acad. Sci. Fenn. Series A. I. Mathematica, vol. 10, pp. 515–526, (1985).
[2] L. Bers. “On moduli of Riemann surfaces”. (Mimeographed lecture notes), Eidgenossische Technische Hochschule, Zurig, (1964).
[3] H. Helling. “Diskrete Untergruppen von SL2(R)”. Inventiones Math. 17, pp. 217-299, (1972).
[4] R.A. Hidalgo. “The noded Schottky space”. Proc. London Math. Soc. 73, pp. 385-403, (1996).
[5] R.A. Hidalgo. “Fixed point parameters for Fuchsian groups of type (1; 2; 0)”. Accepted for publication in Revista Scientia.
[6] C. L. Earle. “Some intrinsic coordinates on Teichmüller space”. Proc. Amer. Math. Soc. 83, pp. 527–531, (1981).
[7] C. L. Earle and A. Marden. “Geometric complex coordinates for Teichmüller space” (to appear)
[8] I. Kra. “Horocyclic coordinates for Riemann surfaces and moduli spaces. I: Teichmüller and Riemann spaces of Kleinian groups”. J. of the Amer. Math. Soc. 3, pp. 499–578, (1990).
[9] I. Kra, “Non-variational global coordinates for Teichmüller spaces”, in Holomorphic Functions and Moduli II, Math. Sci. Res. Inst. Publ., vol. 11, Springer, Berlin, Tokyo, pp. 221–249, (1988).
[10] I. Kra and B. Maskit. “The deformation space of a Kleinian group”. Amer. J. Math. 103, pp. 1065–1102, (1980).
[11] A. Marden. “Geometric complex coordinates for Teichmüller space”. In Mathematical Aspects of String Theory (S. T. Yau, ed.), World Scientific, Singapore, pp. 341–364, (1987).
[12] B. Maskit. “Moduli of marked Riemann surfaces”. Bull. Amer. Math. Soc. 80, pp. 773–777, (1974).
[13] B. Maskit. “Parameters for Fuchsian groups I: Signature (0,4)”. Holomorphic Functions and Moduli II, pp. 251–265. Math. Sci. Res. Inst. Pub. 11. Springer - Verlag, New York, (1988).
[14] B. Maskit. “Parameters for Fuchsian groups II: topological type (1,1)”. Annal. Acad. Sci. Fenn. Ser. A.I. 14, pp. 265–275, (1990).
[15] B. Maskit. “Explicit Matrices for Fuchsian groups”. Preprint IHES/M/92/6 Février (1992).
[16] B. Maskit. Kleinian Groups. Grundlehren der Mathematischen Wissenschaften, vol. 287,Springer - Verlag, Berlin, Heildelberg, New York, (1988).
[17] C. Min. “New parameters of Teichmüller spaces of Riemann surfaces of genus two”. Ann. Acad. Scie. Fenn., Series A.I. Mathematica, Vol.17, (1992).
[18] S. Nag. The complex analytic theory of Teichmüller spaces. Canadian Mathematical Society Series of Monographs and Advances texts. AWiley Interscience Pub. (1988).
[19] M. Seppala and T. Sorvali. “On geometric parametrization of Teichmüller spaces”. Ann. Acad. Sci. Fenn. Series A. I. Mathematica, vol. 10, pp. 515–526, (1985).
Published
2017-06-14
How to Cite
[1]
R. A. Hidalgo and G. Labbé, “Fixed points parameters for Teichmüller space of closed Riemann surfaces”, Proyecciones (Antofagasta, On line), vol. 19, no. 1, pp. 65-94, Jun. 2017.
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