DIAGRAMS FOR RELATIVE TRISECTIONS

We establish a correspondence between trisections of smooth, compact, oriented 4-manifolds with connected boundary and diagrams describing these trisected 4-manifolds. Such a diagram comes in the form of a compact, oriented surface with boundary together with three tuples of simple closed curves, with possibly fewer curves than the genus of the surface, satisfying a pairwise condition of being standard. This should be thought of as the 4-dimensional analog of a sutured Heegaard diagram for a sutured 3-manifold. We also give many foundational examples.