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The limit set of discrete subgroups of PSL(3, ℂ)

Published online by Cambridge University Press:  02 September 2010

WALDEMAR DEL JESÚS BARRERA VARGAS ,
ANGEL CANO CORDERO  and
JUAN PABLO NAVARRETE CARRILLO
WALDEMAR DEL JESÚS BARRERA VARGAS
Affiliation:
Universidad Autónoma de Yucatán, Facultad de Matematicas, Periférico Norte Tablaje Cat 13615 Chuburná Hildalgo, Mérida, Yucatán, México. e-mail: bvargas@uady.mx
ANGEL CANO CORDERO
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, Brazil. e-mail: acano@impa.br
JUAN PABLO NAVARRETE CARRILLO
Affiliation:
Universidad Autónoma de Yucatán, Facultad de Matematicas, Periférico Norte Tablaje Cat 13615 Chuburná Hildalgo, Mérida, Yucatán, México. e-mail: jp.navarrete@uady.mx
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Abstract

If Γ is a discrete subgroup of PSL(3, ℂ), it is determined the equicontinuity region Eq(Γ) of the natural action of Γ on ℙ2ℂ. It is also proved that the action restricted to Eq(Γ) is discontinuous, and Eq(Γ) agrees with the discontinuity set in the sense of Kulkarni whenever the limit set of Γ in the sense of Kulkarni, Λ(Γ), contains at least three complex lines in general position. Under some additional hypothesis, it turns out to be the largest open set on which Γ acts discontinuously. Moreover, if Λ(Γ) contains at least four complex lines and Γ acts on ℙ2ℂ without fixed points nor invariant complex lines, then each connected component of Eq(Γ) is a holomorphy domain and a complete Kobayashi hyperbolic space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 1 , January 2011 , pp. 129 - 146
Copyright
Copyright © Cambridge Philosophical Society 2010

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References

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