Multisections and bridge positions in arbitrary dimensions

Sylvain Courte; Delphine Moussard; Qiuyu Ren; Xiaozhou Zhou

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arXiv · 2608.00460

Multisections and bridge positions in arbitrary dimensions

Sylvain Courte·Delphine Moussard·Qiuyu Ren·Xiaozhou Zhou

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Abstract

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 $4$.

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Sylvain Courte, Delphine Moussard, Qiuyu Ren, Xiaozhou Zhou. 2026-08-01. Multisections and bridge positions in arbitrary dimensions. https://arxiv.org/abs/2608.00460

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