Year: 2022
Type: preprint
Abstract: We show the manifolds at infinity of the complex hyperbolic triangle groups $Δ_{3,4,4;\infty}$ and $Δ_{3,4,6;\infty}$,are one-cusped hyperbolic 3-manifolds $m038$ and $s090$ in the Snappy Census respectively.That is,these two manifolds admit spherical CR uniformizations. Moreover, these two hyperbolic 3-manifolds above can be obtained by Dehn surgeries on the first cusp of the two-cusped hyperbolic 3-manifold $m295$ in the Snappy Census with slopes $2$ and $4$ respectively. In general,the main result in this paper allow us to conjecture that the manifold at infinity of the complex hyperbolic triangle group $Δ_{3,4,n;\infty}$ is the one-cusped hyperbolic 3-manifold obtained by Dehn surgery on the first cusp of $m295$ with slope $n-2$.
Source: arXiv (Cornell University)
Authors: Ma, Jiming, Xie, Baohua
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1206532262, G4000309048, G6160687005
OpenAlex ID: W4281479569