"Mass transport on aperiodic tilings"Sadun, LorenzoSuppose that we have two mass distributions on a $d$-dimensional aperiodic tiling, each defined by a local rule such as "put 3 kg on every A tile and 1 kg on every B tile" or "put 5kg on every A tile that is next to a B tile". When is it possible to do a bounded transport from one distribution to the other? When is it possible to do that transport according to a local rule? When is it possible to do that transport in a way that is arbitrarily well approximated by a local rule? All of these questions boil down to questions about the top Cech cohomology of the continuous hull of our tiling. We answer those questions for a wide class of substitution tilings. This is joint work with Michael Kelly. |
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