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Proyecciones (Antofagasta) - ON THE RETROSECTION THEOREM

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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.27 n.1 Antofagasta mayo 2008

http://dx.doi.org/10.4067/S0716-09172008000100003 

Proyecciones Journal of Mathematics
Vol. 27, Nº 1, pp. 29-61, May 2008.
Universidad Católica del Norte
Antofagasta - Chile


ON THE RETROSECTION THEOREM


RUBÉN HIDALGO

Universidad Técnica Federico Santa María, Chile.

Correspondencia a:



Abstract
We survey some old and new results related to the retrosection theorem and some of its extensions to compact Klein surfaces, stable Riemann surfaces and stable Klein surfaces.


Key words : Riemann Surfaces, Klein surfaces, Schottky Groups
Subjclass : 2000, 30F10, 30F40.

REFERENCES
[1] L. V. Ahlfors. Finitely generated Kleinian groups, Amer. J. Math. 86(1964), 413-423; 87 (1965),         [ Links ] 759.
[2] N. L. Alling and N. Greenleaf, N. Foundations of the theory of Klein surfaces. Lect. Notes in Math. 219, Springer-Verlag,         [ Links ] (1971).
[3] L. Bers. Automorphic forms for Schottky groups,. Adv. in Math. 16, pp. 332-361,         [ Links ] (1975).
[4] J. Button. All Fuchsian Schottky groups are classical Schottky groups. Geometry & Topology Monographs 1: The Epstein birthday schrift, pp. 117-125,         [ Links ] (1998).
[5] V. Chuckrow. On Schottky groups with applications to Kleinian groups. Annals of Math. 88, pp. 47-61,         [ Links ] (1968).
[6] D. Hejhal. On Schottky and Teichmüller spaces. Advances in Math. 15, pp. 133-156,         [ Links ] (1975).
[7] B. Heltai. Symmetric Riemann surfaces, torsion subgroups and Schottky coverings. Proc. of the Amer. Math. Soc. 100, pp. 675-682,         [ Links ] (1987).
[8] L. Gerritzen and F. Herrlich. The extended Schottky space. J. Reine Angew. Math. 389, pp. 190-208,         [ Links ] (1988).
[9] R. A. Hidalgo The Noded Schottky Space. Proc. London Math. Soc. 3, pp. 385-403,         [ Links ] (1996).
[10] R. A. Hidalgo. Noded Fuchsian groups I. Complex variables, 36, pp. 45-66,         [ Links ] (1998).
[11] R. A. Hidalgo. Kleinian groups with an invariant Jordan curve: Jgroups. Pacific Journal of Math. 169, pp. 291-309,         [ Links ] (1995).
[12] R. A. Hidalgo. Schottky uniformization of stable symmetric Riemann surfaces. Notas de la Sociedad Matemática de Chile (NS) No. 1, pp. 82-91,         [ Links ] (2001).
[13] R. A. Hidalgo. Automorphisms of Schottky type. Ann. Acad. Scie.Fenn. Mathematica 30, pp. 183-204,         [ Links ] (2005).
[14] R. A. Hidalgo. Noded function groups. Complex geometry of groups (Olmué, 1998), 209-222, Contemp. Math., 240, Amer. Math. Soc.,Providence, RI,         [ Links ] (1999).
[15] R. A. Hidalgo and B. Maskit. On Neoclassical Schottky groups. Trans. of the Amer. Math. Soc. 358, pp. 4765 - 4792,         [ Links ] (2006).
[16] R. A. Hidalgo and B. Maskit. On Klein-Schottky groups. Pacific J. of Math. (2) 220, pp. 313-328,         [ Links ] (2005).
[17] R. A. Hidalgo and B. Maskit. Extended Schottky groups. Pre         [ Links ] print.
[18] P. Koebe. Über die Uniformisierung der Algebraischen Kurven II. Math. Ann. 69 (1910),1-81,         [ Links ] (1910).
[19] P. Koebe. Über die Uniformisierung reeller algebraischer Kurven. Nachr. Akad. Wiss. Goettingen, pp. 177-190,         [ Links ] (1907).
[20] I.Kra. Automorphic forms and Kleinian groups, Benjamin, New York,         [ Links ] (1972).
[21] I. Kra. Horocyclic coordinates for Riemann surfaces and moduli spaces of Kleinian groups. J. Amer. Math. Soc. 3 (1990), 49         [ Links ] 9-578.
[22] A. Marden. Schottky groups and circles. Contribution to Analysis, a collection of papers dedicated to Lipman Bers (L.V. Ahlfors a.o., Eds.),Academic Press, New York 1974, 27         [ Links ] 3-278.
[23] B. Maskit. Kleinian Groups. Springer-Verlag,         [ Links ] 1988.
[24] B. Maskit. On free Kleinian groups. Duke Math. J. 48 (1981), 75         [ Links ] 5-765.
[25] B. Maskit. A characterization of Schottky groups. J. d’Analyse Math. 19 (1967), 22         [ Links ] 7-230.
[26] B. Maskit. On the classification of Kleinian groups:I. Koebe groups. Acta Math. 135, pp. 249-270,         [ Links ] (1975).
[27] B. Maskit. On the classification of Kleinian groups:II. Signatures. Acta Math. 138, pp. 17-42,         [ Links ] (1977).
[28] B. Maskit. On a class of Kleinian groups. Ann. Acad. Sci. Fenn. Ser. A I Math.         [ Links ] (1969).
[29] B. Maskit. Self-maps on Kleinian groups. Amer. J. Math. XCIII, pp. 840-856,         [ Links ] (1971).
[30] D. Mumford. Stability of projective varieties, L’enseignement math. 23, pp. 39-110,         [ Links ] (1977).
[31] S. Nag, The Complex Analytic Theory of Teichmüller Spaces (Wiley, New York,         [ Links ] (1988)).
[32] H. Sato. On a paper of Zaroow. Duke Math. J. 57, pp. 205-209,         [ Links ] (1988).
[33] H. Yamamoto. An example of a nonclassical Schottky group. Duke Math. J. 63, pp. 193-197,         [ Links ] (1991).
[34] R. Zarrow. Classical and nonclassical Schottky groups. Duke Math. J. 42, pp. 717-724,         [ Links ] (1975).

RUBÉN HIDALGO
Departamento de Matemática
Universidad Técnica Federico Santa María,
Valparaíso
Chile
e-mail : mailto:ruben.hidalgo@usm.cl

Received : May 2006. Accepted : March 2008