Complex hyperbolic free groups with many parabolic elements

Parker, John R.; Will, Pierre

Abstract

We consider in this work representations of the of the fundamental group of the 3-punctured sphere in PU(2,1) such that the boundary loops are mapped to PU(2,1) . We provide a system of coordinates on the corresponding representation variety, and analyse more specifically those representations corresponding to subgroups of (3,3,∞) -groups. In particular we prove that it is possible to construct representations of the free group of rank two $\la a,b\ra$ in PU(2,1) for which a , b , ab , ab −1 , ab 2 , a 2 b and [a,b] all are mapped to parabolics.

Citation

Parker, J. R., & Will, P. (2015). Complex hyperbolic free groups with many parabolic elements. In Geometry, groups and dynamics : ICTS program : groups, geometry and dynamics, December 3-16, 2012, Almora, India (327-348). https://doi.org/10.1090/conm/639/12782

• Conference Name: Groups, Geometry and Dynamics
• Conference Location: Almora, Uttarakhand, India
• Start Date: Dec 3, 2012
• End Date: Dec 16, 2012
• Publication Date: May 27, 2015
• Deposit Date: Oct 20, 2014
• Publicly Available Date: Oct 21, 2014
• Pages: 327-348
• Series Title: Contemporary mathematics
• Series Number: 639
• Series ISSN: 0271-4132,1098-3627
• Book Title: Geometry, groups and dynamics : ICTS program : groups, geometry and dynamics, December 3-16, 2012, Almora, India.
• DOI: https://doi.org/10.1090/conm/639/12782
• Related Public URLs: http://arxiv.org/abs/1312.3795