4-流形的简化（2，0）-三等分中的垂直3-流形
Vertical 3-manifolds in simplified (2, 0)-trisections of 4-manifolds
摘要：
我们将简化的$(2, 0)$ -三分映射的平面弧的原像作为$3$-流形进行分类，我们称之为垂直$3$ -流形。这样的$3$ -流形是特定$6$弧上垂直$3$ -流形的$6$ -元组的连通和。因此，我们表明，每一个$6$ -元组确定源$4$ -流形唯一的方向反转的同胚。我们还证明了，与简化的$(2, 0)$ -三分映射的垂直$3$ -流形的和是透镜空间的事实相反，存在无穷多个简化的$(2, 0)$ - $4$ -截面映射允许双曲垂直$3$ -流形.
英文摘要：
We classify the $3$-manifolds obtained as the preimages of arcs on the plane for simplified $(2, 0)$-trisection maps, which we call vertical $3$-manifolds. Such a $3$-manifold is a connected sum of a $6$-tuple of vertical $3$-manifolds over specific $6$ arcs. Consequently, we show that each of the $6$-tuples determines the source $4$-manifold uniquely up to orientation reversing diffeomorphisms. We also show that, in contrast to the fact that summands of vertical $3$-manifolds of simplified $(2, 0)$-trisection maps are lens spaces, there exist infinitely many simplified $(2, 0)$-$4$-section maps that admit hyperbolic vertical $3$-manifolds.
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