In this paper, it is shown that every closed hyperbolic 3-manifold contains an immersed quasi-Fuchsian closed subsurface of odd Euler characteristic. The construction adopts the good pants method, and the primary new ingredient is an enhanced version of the connection principle, which allows one to connect any two frames with a path of frames in a prescribed relative homology class of the frame bundle. The existence result is applied to show that every uniform lattice of $\mathrm{PSL}(2,\mathbb{C})$ admits an exhausting nested sequence of sublattices with exponential homological torsion growth. However, the constructed sublattices are not normal in general.

中文翻译：

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在闭合双曲线 $3$-流形中浸入奇欧拉特征的准 Fuchsian 曲面

在本文中，证明了每个闭合双曲 3-流形都包含一个奇欧拉特性的浸入式准 Fuchsian 闭合次表面。该结构采用良好的裤子方法，主要的新成分是连接原理的增强版本，它允许将任意两个框架与框架束的规定相对同源类中的框架路径连接起来。应用存在性结果表明，$\mathrm{PSL}(2,\mathbb{C})$ 的每一个均匀格都承认具有指数同调扭转增长的穷尽嵌套子格序列。然而，构造的子晶格一般不正常。