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Complex hyperbolic free groups with many parabolic elements.

Parker, John R. and Will, Pierre (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. , pp. 327-348. Contemporary mathematics. (639).


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.

Item Type:Book chapter
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Publisher 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.
Date accepted:No date available
Date deposited:21 October 2014
Date of first online publication:2015
Date first made open access:No date available

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