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• W3100711267 startingPage "3391" @default.
• W3100711267 abstract "We study subgroups of ${rm PU}(2,1)$ generated by two non-commuting unipotent maps $A$ and $B$ whose product $AB$ is also unipotent. We call $mathcal{U}$ the set of conjugacy classes of such groups. We provide a set of coordinates on $mathcal{U}$ that make it homeomorphic to $mathbb{R}^2$ . By considering the action on complex hyperbolic space $mathbf{H}^2_{mathbb{C}}$ of groups in $mathcal{U}$, we describe a two dimensional disc ${mathcal Z}$ in $mathcal{U}$ that parametrises a family of discrete groups. As a corollary, we give a proof of a conjecture of Schwartz for $(3,3,infty)$-triangle groups. We also consider a particular group on the boundary of the disc ${mathcal Z}$ 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." @default.
• W3100711267 created "2020-11-23" @default.
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• W3100711267 date "2017-08-31" @default.
• W3100711267 modified "2023-10-01" @default.
• W3100711267 title "A complex hyperbolic Riley slice" @default.
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• W3100711267 doi "https://doi.org/10.2140/gt.2017.21.3391" @default.
• W3100711267 hasPublicationYear "2017" @default.
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