#### Vol. 294, No. 2, 2018

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Diagrams for relative trisections

### Nickolas A. Castro, David T. Gay and Juanita Pinzón-Caicedo

Vol. 294 (2018), No. 2, 275–305
##### Abstract

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.

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