2026/08/01 by Sylvain Courte, Delphine Moussard, Qiuyu Ren +1
Mathematics · #math.GT #msc:57R65 #msc:57R40 #msc:57Q99
27 pages, 9 figures in color
arxiv created 2026/08/01 · arxiv updated 2026/08/04
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.