Spherical CR uniformization of the magic 3-manifold
Abstract
We show the 3-manifold at infinity of the complex hyperbolic triangle group $\Delta_{3,\infty,\infty;\infty}$ is the three-cusped "magic" 3-manifold $6_1^3$. We also show the 3-manifold at infinity of the complex hyperbolic triangle group $\Delta_{3,4,\infty;\infty}$ is the two-cusped 3-manifold $m295$ in the Snappy Census, which is a 3-manifold obtained by Dehn filling on one cusp of $6_1^3$. In particular, hyperbolic 3-manifolds $6_1^3$ and $m295$ admit spherical CR uniformizations. These results support our conjecture that the 3-manifold at infinity of the complex hyperbolic triangle group $\Delta_{3,n,m;\infty}$ is the one-cusped hyperbolic 3-manifold from the "magic" $6_1^3$ via Dehn fillings with filling slopes $(n-2)$ and $(m-2)$ on the first two cusps of it.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.06668
- arXiv:
- arXiv:2106.06668
- Bibcode:
- 2021arXiv210606668M
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- 64 pages, 34 figures. Comments are welcome!