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

Let $BK$ be the symplectic four-manifold constructed in the paper, and let $V_n$ be the sequence of exotic four-manifolds obtained from $BK$, with $V_1=BK$. 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 exotic four-manifolds $V_n$ have equivalent genus functions. The manifolds are distinguished by their Seiberg–Witten values, but the genus functions cannot currently be compared because their values on most homology classes of negative self-intersection are unknown.