Fixed point parameters for Mobius groups


  • Rubén A. Hidalgo Universidad Técnica Federico Santa María.



Groups, Möbius transformations, complex parameters, algebraic spaces, grupos, transformaciones de Moebius, parámetros complejos, espacios algebraicos.


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.

Author Biography

Rubén A. Hidalgo, Universidad Técnica Federico Santa María.

Departamento de Matemática.


[1] W. Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Mathematics 820, Springer, (1980).

[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).



How to Cite

R. A. Hidalgo, “Fixed point parameters for Mobius groups”, Proyecciones (Antofagasta, On line), vol. 19, no. 2, pp. 157-196, Jun. 2017.