@article { ,
title = {A complex hyperbolic Riley slice},
abstract = {We study subgroups of PU(2,1) generated by two non-commuting unipotent maps A and B whose product AB is also unipotent. We call U the set of conjugacy classes of such groups. We provide a set of coordinates on U that make it homeomorphic to R2 . By considering the action on complex hyperbolic space H2C of groups in U, we describe a two dimensional disc Z in U that parametrises a family of discrete groups. As a corollary, we give a proof of a conjecture of Schwartz for (3,3,∞)-triangle groups. We also consider a particular group on the boundary of the disc Z where the commutator [A,B] is also unipotent. We show that the boundary of the quotient orbifold associated to the latter group gives a spherical CR uniformisation of the Whitehead link complement.},
doi = {10.2140/gt.2017.21.3391},
eissn = {1364-0380},
issn = {1465-3060},
issue = {6},
journal = {Geometry and Topology},
note = {EPrint Processing Status: Full text deposited in DRO},
pages = {3391-3451},
publicationstatus = {Published},
publisher = {Mathematical Sciences Publishers (MSP)},
volume = {21},
year = {2017},
author = {Parker, John R. and Will, Pierre}
}