169 research outputs found
Groups generated by two elliptic elements in PU(2,1)
Let and be two elliptic elements in of order
and respectively, where . We prove that if the distance
between the complex lines or points fixed by and is large
than a certain number, then the group is discrete nonelementary and
isomorphic to the free product .Comment: 9 page
The topology of the Eisenstein-Picard modular surface
The Eisenstein-Picard modular surface is the quotient space of the
complex hyperbolic plane by the modular group . We determine the global topology of as a 4-orbifold
Spherical CR uniformization of the "magic" 3-manifold
We show the 3-manifold at infinity of the complex hyperbolic triangle group
is the three-cusped "magic" 3-manifold
. We also show the 3-manifold at infinity of the complex hyperbolic
triangle group is the two-cusped 3-manifold
in the Snappy Census, which is a 3-manifold obtained by Dehn filling on one
cusp of . In particular, hyperbolic 3-manifolds and admit
spherical CR uniformizations.
These results support our conjecture that the 3-manifold at infinity of the
complex hyperbolic triangle group is the one-cusped
hyperbolic 3-manifold from the "magic" via Dehn fillings with filling
slopes and on the first two cusps of it.Comment: 66 pages, 34 figures. Comments are welcome
A uniformizable spherical CR structure on a two-cusped hyperbolic 3-manifold
Let be the complex hyperbolic
triangle group. In this paper we give a proof of a conjecture of
Schwartz for . That is is discrete and faithful if and only if is
nonelliptic. When is parabolic, we show that the even subgroup
is the holonomy representation of a
uniformizable spherical CR structure on the two-cusped hyperbolic 3-manifold
in SnapPy notation
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