DOI: 10.1112/jlms.70736 ISSN: 0024-6107

Multisections of higher‐dimensional manifolds

Fathi Ben Aribi, Sylvain Courte, Marco Golla, Delphine Moussard
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Abstract

Generalizing Heegaard splittings of 3‐manifolds and Gay–Kirby trisections of 4‐manifolds, we consider multisections of higher‐dimensional smooth (or PL) closed orientable manifolds, namely decompositions into 1‐handlebodies whose subcollections intersect along 1‐handlebodies, with global intersection a closed surface. With such a multisection one can associate a diagram. We prove that a multisection diagram determines a unique PL‐manifold in all dimensions and a unique smooth manifold up to dimension 6. Further, we show that any closed orientable smooth 5‐manifold admits a multisection.

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