Trisections of PL 4-Manifolds Arising from Colored Triangulations

Abstract 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 $$\mathbb {S}^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> </mml:math> , 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.