Multisections of higher-dimensional manifolds
Abstract
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.
Cite
@article{arxiv.2303.08779,
title = {Multisections of higher-dimensional manifolds},
author = {Fathi Ben Aribi and Sylvain Courte and Marco Golla and Delphine Moussard},
journal= {arXiv preprint arXiv:2303.08779},
year = {2024}
}
Comments
24 pages, 18 figures. The exposition has been improved, we added the example of the 5-dimensional real projective space, and a section with the computation of the homology of a multisected manifold from a diagram