AI 中文总结
该研究针对SnapPy普查中的双尖点双曲3-流形s782，通过对比相关三角群的区域组合结构，证明对任意n≥5，其二尖点按指定斜率Dehn填充后可获得球形CR单值化。
AI 中文摘要
设s782为SnapPy普查中的双尖点双曲3-流形，其球形CR单值化已由\uc810{JWX2023}利用复双曲三角群Δ_{4,4,∞;∞}的Ford区域建立。通过对比Δ_{4,4,∞;∞}的Ford区域与Δ_{4,4,n;∞}的Dirichlet区域的组合结构，我们证明：对每个n≥5，s782在其二尖点处沿斜率(n-1)m₁+l₁进行Dehn填充后，可获得球形CR单值化，其中(m₁,l₁)为SnapPy记号下尖点的子午线-经线系统。
英文摘要
Let $s782$ be the 2-cusped hyperbolic 3-manifold in the SnapPy census. Its spherical CR uniformization was established in \cite{JWX2023} using the Ford domain of the complex hyperbolic triangle group $Δ_{4,4,\infty;\infty}$. By comparing the combinatorial structures of the Ford domain of $Δ_{4,4,\infty;\infty}$ and the Dirichlet domain of $Δ_{4,4,n;\infty}$, we prove that for each $n \geq 5$, the Dehn filling of $s782$ along the slope $(n-1)\mathcal{m}_1 + \mathcal{l}_1$ on its second cusp admits a spherical CR uniformization, where $(\mathcal{m}_1, \mathcal{l}_1)$ denotes the meridian-longitude system of a cusp in SnapPy notation.
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