Pattern Equivariant Functions, Deformations and Equivalence of Tiling Spaces
نویسنده
چکیده
We reinvestigate the theory of deformations of tilings using P -equivariant cohomology. In particular we relate the notion of asymptotically negligible shape functions introduced by Clark and Sadun to weakly P -equivariant forms. We then investigate more closely the relation between deformations of patterns and homeomorphism or topological conjugacy of pattern spaces.
منابع مشابه
Pattern Equivariant Cohomology and Theorems of Kesten and Oren
In 1966 Harry Kesten settled the Erdős-Szüsz conjecture on the local discrepancy of irrational rotations. His proof made heavy use of continued fractions and Diophantine analysis. In this paper we give a purely topological proof Kesten’s theorem (and Oren’s generalization of it) using the pattern equivariant cohomology of aperiodic tiling spaces.
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