Multisections of higher-dimensional manifolds

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.