AI 中文总结
该研究证明闭流形的多截面在任意维数下均存在，且多截面流形中余维至少2的子流形可置于合适桥位置，推广了低维相关结果。
AI 中文摘要
多截面由Ben Aribi、Courte、Golla和Moussard定义，用于将闭流形分解为1-柄体，是Heegaard分裂和三分法的推广。此前仅知其在不超过5维时存在，本文证明闭流形的多截面在任意维数下均存在；还证明多截面流形中余维至少2的子流形总能置于合适的桥位置，推广了4维桥三分法的存在性结果。
英文摘要
Multisections were defined by Ben Aribi--Courte--Golla--Moussard as a way to decompose closed manifolds into $1$-handlebodies, which is a generalization of Heegaard splittings and trisections. Previously, their existence was only known in dimensions up to $5$. We show that multisections exist for closed manifolds in arbitrary dimensions. We also show that submanifolds of codimension at least $2$ in multisected manifolds can always be put into an appropriate bridge position, generalizing the existence result on bridge trisections in dimension $4$.
Comments27 pages, 9 figures in color
