Complex hyperbolic free groups with many parabolic elements

2013/12/13 by Parker, John R., Will, Pierre · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1312.3795

Abstract

We consider in this work representations of the of the fundamental group of the 3-punctured sphere in \rm PU(2,1) such that the boundary loops are mapped to \rm 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 \rm PU(2,1) for which a, b, ab, ab^-1, ab², a²b and [a,b] all are mapped to parabolics.

Cited by

• Horn's problem in PU(n,1)

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