A Homeomorphism Invariant for Substitution Tiling Spaces

Details A Homeomorphism Invariant for Substitution Tiling Spaces A Homeomorphism Invariant for Substitution Tiling Spaces

2000-08-22

arxiv.org/abs/math/0008171v1

Mathematics

Dynamical Systems

32 pages, including 9 embedded figures

Scientific paper

We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of Cech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as of intuitive value.

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