Complex hyperbolic free groups with many parabolic elements

Parker, John R.; Will, Pierre

doi:10.1090/conm/639/12782

Complex hyperbolic free groups with many parabolic elements

Parker, John R.; Will, Pierre

Authors

Professor John Parker j.r.parker@durham.ac.uk
Professor

Pierre Will

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

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Copyright Statement
© 2015 American Mathematical Society. First published in 'Geometry, groups and dynamics: ICTS program: groups, geometry and dynamics, December 3-16, 2012, Almora, India.' in Contemporary mathematics series, 639, 2015, published by the American Mathematical Society.