Trisections and Ozsv\'ath-Szab\'o Four-Manifold Invariants

Given a smooth, compact four-manifold $X$, we demonstrate how to use the data of a trisection map $\pi:X^{4} \to \mathbb{R}^{2}$ to compute the induced cobordism maps on Heegaard Floer homology. A result of Gay and Kirby shows that such a map $\pi$ induces an open book decomposition on the boundary of $X$, and we show how to recover the Ozsv\'ath-Szab\'o contact invariant in this setting, along with its image under the cobordism maps.