Tiling Spaces are Inverse Limits

Details Tiling Spaces are Inverse Limits Tiling Spaces are Inverse Limits

2002-10-11

arxiv.org/abs/math/0210179v1

Mathematics

Dynamical Systems

Latex, 6 pages, including one embedded figure

Scientific paper

10.1063/1.1613041

Let M be an arbitrary Riemannian homogeneous space, and let Omega be a space of tilings of M, with finite local complexity (relative to some symmetry group Gamma) and closed in the natural topology. Then Omega is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Gamma. This result extends previous results of Anderson and Putnam, of Ormes, Radin and Sadun, of Bellissard, Benedetti and Gambaudo, and of G\"ahler. In particular, the construction in this paper is a natural generalization of G\"ahler's.

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