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Pattern equivariant functions, deformations and equivalence of tiling spaces

Published online by Cambridge University Press:  01 August 2008

JOHANNES KELLENDONK
JOHANNES KELLENDONK*
Affiliation:
Université de Lyon, Université Lyon 1, CNRS, UMR 5208 Institut Camille Jordan, Batiment du Doyen Jean Braconnier, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
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Abstract

We re-investigate 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 4 , August 2008 , pp. 1153 - 1176
Copyright
Copyright © 2008 Cambridge University Press

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