Trisections of PL 4-Manifolds Arising from Colored Triangulations

The purpose of the present paper is twofold: first to extend to non-orientable compact 4-manifolds the notion of gem-induced trisection, directly obtained from colored triangulations (or, equivalently, from colored graphs encoding them, called gems); second to prove that, both in the orientable and non-orientable case, if the boundary is homeomorphic to a connected sum of sphere bundles over S^1, gem-induced trisections naturally give rise to trisections of the corresponding closed 4-manifold. As a consequence, an estimation of the trisection genus of any closed orientable 4-manifold is obtained via colored triangulations, in terms of the combinatorial properties of a Kirby diagram representing it.