Multisections of surface bundles and bundles over the circle
arXiv:2305.05619
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.
16 pages, 17 figures. The example of the 2-sphere bundles over the 4-sphere was false and has been corrected (Figure 7 and associated text)