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Suppose that we have a repetitive and aperiodic tiling $\bf T$ of$\mathbb{R}^n$, and two mass distributions $f_1$ and $f_2$ on $\mathbb{R}^n$,each pattern equivariant with respect to $\bf T$. Under what circumstances isit possible to do a bounded transport from $f_1$ to $f_2$? When is it possibleto do this transport in a strongly or weakly pattern-equivariant way? We reducethese questions to properties of the \v Cech cohomology of the hull of $\bf T$,properties that in most common examples are already well-understood.

Pattern Equivariant Mass Transport in Aperiodic Tilings and Cohomology