5 problems

Let $A_1,\dots,A_m$ be the original maps, let $\mathcal{W}$ be a Whitney tower on them, and let $\tau_n(\mathcal{W})$ be its intersection tree, regarded as an element of the quotie…

Let $X$ be a simply connected $4$-manifold, and let $A=A_1,A_2,A_3,A_4$ support an order-$2$ non-repeating Whitney tower $\mathcal W$. Let $\lambda_2(A)$ be the order-$2$ intersect…

Let $X$ be a $4$-manifold and let $A:\amalg^4 S^2\to X$ be a quadruple of immersed $2$-spheres. Suppose that $A$ admits an order $2$ non-repeating Whitney tower $\mathcal{W}$, and…

Let $A:\Sigma\to X$ be a collection of immersed $2$-spheres in a $4$-manifold, and suppose that $\lambda_n(A):=\lambda_n(\mathcal{W})$ is defined using an order $n$ non-repeating W…

Let $A$ be an immersion of $2$-spheres into a $4$-manifold, let $\mathrm{INT}_n(A)$ denote the relations needed to make the obstruction $4\lambda_n(\mathcal{W})4$ independent of th…