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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 396
Projection Quasicrystals II: Versus Substitution Tilings A.H. Forrest, J.R. Hunton and J. Kellendonk
This is the second paper in a short series devoted to the study and application of topological invariants for projection (strip) method quasiperiodic tilings and patterns. In the first paper we study in detail a range of commutative and non-commutative spaces that can be associated to such patterns. In this paper we use these constructions to define and discuss topological invariants for projection patterns variously in terms of groupoid cohomology, C^* K-theory, Czech cohomology and dynamical or group cohomology. We show that, up to order, all these invariants are essentially the same, hence providing convenient computational methods for the non-commutative invariants. We also show that these invariants give a useful obstruction to a pattern being a substitution system and we analyse the qualitative nature of these invariants with this property in mind
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