  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.
