  In these notes, we describe several geometric interpretations of $H^2(X)$
when $X$ is a trisected 4-manifold. The main insight is that, by analogy with
Hodge theory and sheaf cohomology in algebraic geometry, classes in $H^2(X)$
can be usefully interpeted as $"(1,1)"$-classes. These notes formed the first
half of an aborted seminar on symplectic trisections at the Max Planck
Institute for Mathematics during Spring 2020.
