Trisections of Nonorientable 4-Manifolds

We study trisections of smooth compact nonorientable 4 -manifolds and introduce trisections of nonorientable 4 -manifolds with boundary. In particular, we prove a nonorientable analogue of a classical theorem of Laudenbach-Po & eacute;naru and analogues for some well-known theorems from 3 -manifold topology. As a consequence, trisection diagrams and Kirby diagrams of closed nonorientable 4manifolds exist. We discuss how the theory of trisections may be adapted to the setting of nonorientable 4 -manifolds with many examples.