The equivalent genus-function conjecture for the exotic four-manifolds $Z_n$

Let $AP$ be the four-manifold constructed in the paper, and let $Z_n$ be the infinite family of exotic four-manifolds obtained by replacing the final Luttinger surgery with torus surgery of coefficient $n$. For a smooth four-manifold $X$, write $g_X$ for its genus function, assigning to each homology class the minimal genus of an embedded representative. The equivalent genus-function conjecture. The genus functions of the exotic four-manifolds $Z_n$ are all equivalent to $g_{AP}$. The constructions establish equality for the homology classes for which the genus function has been identified, while the full equivalence remains open because the genus function is not known on all classes.