SciELO - Scientific Electronic Library Online

 
vol.21 número1ASYMPTOTIC EQUILIBRIUM FOR CERTAIN TYPE OF DIFFERENTIAL EQUATIONS WITH MAXIMUMON FUZZY WEAKLY SEMIOPEN FUNCTIONS índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

Compartir


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.21 n.1 Antofagasta mayo 2002

http://dx.doi.org/10.4067/S0716-09172002000100003 

Proyecciones
Vol. 21, N o 1, pp. 21-50, May 2002.
Universidad Católica del Norte
Antofagasta - Chile

SOME SPECIAL KLEINIAN GROUPS
AND THEIR ORBIFOLDS

 

RUBÉN HIDALGO
Universidad Técnica Federico Santa María - Chile

 

Abstract

Let us consider an abstract group with the following presentation

. We provide conditions in order to find a faithful, discrete and geometrically finite representation that is, to represent G as a group of isometries of the hyperbolic three space H 3 .

References

[1] H.S.M. Coxeter and W.O.J. Moser. Generators and Relations for Discrete Groups. Springer-Verlag, (1980).        [ Links ]

[2] M. Hagelberg. Generalized triangle groups and 3 ¡ dimensional orbifolds. Amer. Math. Soc. Contemp. Math. 184, pp. 185-192,(1995).        [ Links ]

[3] M. Hagelberg, M. MacClaughlan and G. Rosenberger. On discrete generalized triangle groups. Proc Edinburg Math. Soc., II 38, pp.397-412, (1995).        [ Links ]

[4] M. Hagelberg and A.Y. Vesnin. On a family of hyperbolic dihedral µ(p=q)-orbifolds. Vychisl. Sist. 155, pp. 15-36 (Russian), (1996).        [ Links ]

[5] H. Helling, J. Mennicke and E.B. Vinberg. On some general tri-angle groups and 3 ¡ dimensional orbifolds. Trans. Mosc. Math.Soc., pp. 1-21, (1995).        [ Links ]

[6] M. Hagelberg and R. Hidalgo. Generalized Coxeter groups and their orbifolds. Revista Matem´atica Iberoamericana 13 (1997), pp.543-566, (1997).        [ Links ]

[7] B. Maskit. Kleinian groups. Springer-Verlag, Berlin and New York, (1972).        [ Links ]

[8] J.G. Ractliffe. Foundations of Hyperbolic Manifolds. Graduate Texts in Math., Springer-Verlag, (1994).        [ Links ]

[9] W. Scott. The geometries of three manifolds. Bull. London Math. Soc. 15, pp. 407-487, (1983).        [ Links ]

[10] W.P. Thurston. The geometry and topology of 3 ¡ manifolds. Lecture Notes, Princeton Univ.., (1980).        [ Links ]

[11] S.V. Tsaranov. On a generalization of Coxeter groups. Alg. Groups Geom. 6, 281-318 (1989).        [ Links ]

[12] . Finite generalize Coxeter groups. Alg. Groups Geom. 6, pp. 421- 452, (1989).        [ Links ]

Received : May 2001.

Rubén Hidalgo
Departamento de Matemática
Universidad Técnica Federico Santa María
Casilla 110-V
Valparaíso
Chile
e-mail : rhidalgo@mat.utfsm.cl


This work was partially supported by projects Fondecyt 1000715, Fondecyt
1010093 and UTFSM 12.01.22.

Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons