Three-manifolds at infinity of complex hyperbolic orbifolds

2022/05/23 by Ma, Jiming, Xie, Baohua
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2205.11167

Abstract

We show the manifolds at infinity of the complex hyperbolic triangle groups Δ_3,4,4;∞ and Δ_3,4,6;∞,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;∞ is the one-cusped hyperbolic 3-manifold obtained by Dehn surgery on the first cusp of m295 with slope n-2.

Related

• Spherical CR uniformization of the magic 3-manifold
• Complex Hyperbolic Geometry of Chain Links
• Word hyperbolic Dehn surgery
• Complex hyperbolic triangle groups
• The complete 10-tetrahedra census of orientable cusped hyperbolic 3-manifolds