A Homeomorphism Invariant for Substitution Tiling Spaces
نویسندگان
چکیده
Wederive ahomeomorphism invariant for those tiling spaceswhich aremadeby rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in in¢nitely manyorientations.The invariant is a quotient of C4 ech 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. Mathematics Subject Classi¢cations (2000). 37B50, 52C23, 52C20.
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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 Čech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like ti...
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