2023/03/15 by Fathi Ben Aribi, Aribi, Fathi Ben, Sylvain Courte +5 · 2 citations
Mathematics · #math.GT
paper · pdf · doi:10.48550/arxiv.2303.08779
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.