Kotschick–Morgan wall-crossing polynomiality conjecture

Let $X$ be a smooth simply connected $4$-manifold. For a class $xi\in H^2(X,\mathbb Z)$ defining a wall, an integer $N$, and the associated wall-crossing term $\delta^X_{\xi,N}$, let $Q_X$ denote the quadratic form on $H_2(X,\mathbb Z)$. Kotschick–Morgan conjecture. $\delta^X_{\xi,N}$ is a polynomial in multiplication by $\xi$ and the quadratic form $Q_X$ whose coefficients depend only on $\xi^2$, $N$, and the homotopy type of $X$. This conjecture predicts that the wall-crossing terms are controlled by topological data rather than the particular smooth structure or metric; the supplied text gives no resolution status.