We establish a correspondence between trisections of smooth, compact, oriented
-manifolds
with connected boundary and diagrams describing these trisected
-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
-dimensional
analog of a sutured Heegaard diagram for a sutured
-manifold.
We also give many foundational examples.
Keywords
trisection, open book, Heegaard diagram, monodromy,
3-manifold, 4-manifold