Homological sphere conjecture for differences of Minkowski sums

Let $A$ and $B$ be convex bodies in $\mathbb R^n$. The set $(A+B)\setminus A$ is the difference between a Minkowski sum and one summand. Homological sphere conjecture. The set $(A+B)\setminus A$ is either empty, acyclic, or has the homology of a sphere of dimension $k\in[0,n-1]$. This conjecture asks for an analogue of the paper's acyclicity result for $A\setminus(A+B)$; its resolution is not given here.