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Pré-Publication, Document De Travail Année : 2023

Multisections of higher-dimensional manifolds

Fathi Ben Aribi
  • Fonction : Auteur
Sylvain Courte
  • Fonction : Auteur
Delphine Moussard
  • Fonction : Auteur

Résumé

Generalizing Heegaard splittings of 3-manifolds and 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.

Dates et versions

hal-04266689 , version 1 (31-10-2023)

Identifiants

Citer

Fathi Ben Aribi, Sylvain Courte, Marco Golla, Delphine Moussard. Multisections of higher-dimensional manifolds. 2023. ⟨hal-04266689⟩

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