We show the 3-manifold at infinity of the complex hyperbolic triangle group
Ξ3,β,β;ββ is the three-cusped "magic" 3-manifold
613β. We also show the 3-manifold at infinity of the complex hyperbolic
triangle group Ξ3,4,β;ββ is the two-cusped 3-manifold m295
in the Snappy Census, which is a 3-manifold obtained by Dehn filling on one
cusp of 613β. In particular, hyperbolic 3-manifolds 613β and m295 admit
spherical CR uniformizations.
These results support our conjecture that the 3-manifold at infinity of the
complex hyperbolic triangle group Ξ3,n,m;ββ is the one-cusped
hyperbolic 3-manifold from the "magic" 613β via Dehn fillings with filling
slopes (nβ2) and (mβ2) on the first two cusps of it.Comment: 66 pages, 34 figures. Comments are welcome