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arXiv · 2305.05619

Multisections of surface bundles and bundles over the circle

Delphine Moussard
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Abstract

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.

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Delphine Moussard. 2026-09-09. Multisections of surface bundles and bundles over the circle. https://arxiv.org/abs/2305.05619

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