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A complex hyperbolic Riley slice.

Parker, John R. and Will, Pierre (2017) 'A complex hyperbolic Riley slice.', Geometry and topology., 21 (6). pp. 3391-3451.

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.

Item Type:Article
Full text:Publisher-imposed embargo
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.2140/gt.2017.21.3391
Publisher statement:First published in Geometry & Topology, 21(6), 2017, published by Mathematical Sciences Publishers. © 2017 Mathematical Sciences Publishers. All rights reserved.
Date accepted:28 June 2016
Date deposited:05 July 2016
Date of first online publication:31 August 2017
Date first made open access:06 September 2017

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