On orbit closure decompositions of tiling spaces by the generalized projection method

摘要

Let (E) be the tiling space on a p-dimensional subspace E of R~d with a fixed lattice L by the generalized projection method. By using the dual of the lattice L we will construst explicitly a parameter family of the orbit closure decomposition of (E) and characterize its dimension. As its application we obtain that the parameters of the orbit closure decomposition of (E) correspond to the periods of (E), provided that (E) and (E) are given by the generalized projection method from an integral lattice L.