CONJUGACIES OF MODEL SETS

Let M be a model set meeting two simple conditions: (1) the internal group H is R-n (or a product of R-n and a finite group) and (2) the window W is a finite union of disjoint polyhedra. Then any Delone set with finite local complexity (FLC) that is topologically conjugate to M is mutually locally derivable (MLD) to a model set M' that has the same internal group and window as M, but has a different projection from H x R-d to Rd. In cohomological terms, this means that the group H-an(1) (M, R) of asymptotically negligible classes has dimension n. We also exhibit a counterexample when the second hypothesis is removed, constructing two topologically conjugate FLC Delone sets, one a model set and the other not even a Meyer set.