Fixed point parameters for Mobius groups
DOI:
https://doi.org/10.22199/S0716-09172000000200005Keywords:
Groups, Möbius transformations, complex parameters, algebraic spaces, grupos, transformaciones de Moebius, parámetros complejos, espacios algebraicos.Abstract
Let ?n (respectively, ??) be a free group of rank n (respectively, a free group of countable infinite rank). We consider the space of algebraic representations of the group ?n (respectively, ??) Hom(?n; PGL(2; C)) (respectively, Hom(??; PGL(2; C))). Inside each of these spaces we consider a couple of open and dense subsets. These subsets contain non-discrete groups of Möbius transformations. We proceed to find complex analytic parameters for these spaces given by fixed points.References
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[2] R.A. Hidalgo, The noded Schottky space I, Proc. London Math. Soc. 73, pp. 385-403, (1996)
[3] R. A. Hidalgo and G. Labbe, Fixed point parameters for Teichmüller space of closed Riemann surfaces, Revista Proyecciones 19, pp. 65-94, (2000).
[4] 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).
[5] B. Maskit, Parameters for Fuchsian groups II: topological type (1,1), Annal. Acad. Sci. Fenn. Ser. A.I. 14, pp. 265–275, (1990).
[6] B. Maskit, New parameters for fuchsian groups of genus two. Preprints.
[7] B. Maskit, Kleinian Groups, Grundlehren der Mathematischen Wissenschaften, Vol. 287,Springer - Verlag, Berlin, Heildelberg, New York, (1988).
[8] I. Kra and B. Maskit, The deformation space of a Kleinian group, Amer. J. Math. 103, pp. 1065–1102, (1980).
[9] C. Min, New parameters of Teichmüller spaces of Riemann surfaces of genus two, Ann. Acad. Scie. Fenn., Series A.I. Mathematica, 17 (1992).
Published
2017-06-14
How to Cite
[1]
R. A. Hidalgo, “Fixed point parameters for Mobius groups”, Proyecciones (Antofagasta, On line), vol. 19, no. 2, pp. 157-196, Jun. 2017.
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