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Pattern equivariant functions, deformations and equivalence of tiling spaces

Johannes Kellendonk
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Abstract

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.

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Johannes Kellendonk. 2007-03-06. Pattern equivariant functions, deformations and equivalence of tiling spaces. https://arxiv.org/abs/math/0703156

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