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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

Subgroups of $ PSL(3,\mathbb{C})$ with four lines in general position in its limit set


Authors: W. Barrera, A. Cano and J. P. Navarrete
Journal: Conform. Geom. Dyn. 15 (2011), 160-176
MSC (2010): Primary 37F30, 32Q45; Secondary 37F45, 22E40
Published electronically: October 11, 2011
MathSciNet review: 2846306
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Abstract: In this article we provide an algebraic characterization of the subgroups of $ PSL(3,\Bbb {C})$ for which the maximum number of complex lines in general position contained in its limit set, according to Kulkarni, is equal to four. Also, we give an explicit description of the discontinuity region, according to Kulkarni, of such groups.


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Additional Information

W. Barrera
Affiliation: Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte Tablaje Cat 13615, Mérida, Yucatán, México
Email: bvargas@uady.mx

A. Cano
Affiliation: Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
Address at time of publication: Instituto de Matemáticas (Unidad Cuernavaca), UNAM, Av. Universidad s/n Col. Lomas de Chamilpa, C.P. 62210, Cuernavaca, Morelos, México
Email: angel@impa.br, angel@matcuer.unam.mx

J. P. Navarrete
Affiliation: Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte Tablaje Cat 13615, Mérida, Yucatán, México
Email: jp.navarrete@uady.mx

DOI: http://dx.doi.org/10.1090/S1088-4173-2011-00231-1
PII: S 1088-4173(2011)00231-1
Keywords: Kleinian groups, projective complex plane, discrete groups, limit set
Received by editor(s): November 25, 2010
Published electronically: October 11, 2011
Additional Notes: The second author was partially supported by grants from CNPq.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.