  In this paper, we establish a version of the adjunction inequality for closed
symplectic 4-manifolds. As in a previous paper on the Thom conjecture, we use
contact geometry and trisections of 4-manifolds to reduce this inequality to
the slice-Bennequin inequality for knots in the 4-ball. As this latter result
can be proved using Khovanov homology, we completely avoid gauge theoretic
techniques. This inequality can be used to give gauge-theory-free proofs of
several landmark results in 4-manifold topology, such as detecting exotic
smooth structures, the symplectic Thom conjecture, and exluding connected sum
decompositions of certain symplectic 4-manifolds.
