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A homeomorphism invariant for substitution tiling spaces. (English) Zbl 0997.37006
An invariant of homeomorphism for tiling spaces defined by substitutions of polygonal tiles is constructed. Two specific aspects of the cohomology of the tiling spaces are shown to be easily computable: an ordering on the top-dimensional (Cech) cohomology group (and the result that the positive cone is an invariant), and the algebraic structure induced by the relative orientation group. Several examples are discussed in detail, including new pairs of tilings that can be distinguished by these results.

##### MSC:
 37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010) 52C23 Quasicrystals and aperiodic tilings in discrete geometry 52C20 Tilings in $$2$$ dimensions (aspects of discrete geometry) 46L80 $$K$$-theory and operator algebras (including cyclic theory)
##### Keywords:
aperiodic tiling; topological invariants
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