Multisections of surface bundles and bundles over S1

• Autores: Delphine Moussard
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 69, Nº 1, 2025, págs. 147-161
• Idioma: inglés
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• Resumen

  • A multisection is a decomposition of a manifold into 1-handlebodies, where each subcollection of the pieces intersects along a 1-handlebody except the global intersection, which is a closed surface. These generalizations of Heegaard splittings and Gay-Kirby trisections were introduced by Ben Aribi, Courte, Golla, and the author, who proved in particular that any 5-manifold admits such a multisection. In arbitrary dimension, we show that two classes of manifolds admit multisections: surface bundles and fiber bundles over the circle, whose fiber itself is multisected. We provide explicit constructions, with examples.