Topological Invariants for Projection Method Patterns.

Intro -- Table of Contents -- General Introduction -- I: Topological Spaces and Dynamical Systems -- 1 Introduction -- 2 The projection method and associated geometric constructions -- 3 Topological spaces for point patterns -- 4 Tilings and point patterns -- 5 Comparing II[sub(u)] and II[sub(u)] -- 6 Calculating M P[sub(u)] and M P[sup(u)] -- 7 Comparing M P[sup(u)] with M P[sup(u)] -- 8 Examples and counter-examples -- 9 The topology of the continuous hull -- 10 A Cantor Z[sup(d)] dynamical system -- II: Groupoids, C*-algebras, and their Invariants -- 1 Introduction -- 2 Equivalence of projection method pattern groupoids -- 3 Continuous similarity of projection method pattern groupoids -- 4 Pattern cohomology and K-theory -- 5 Homological conditions for self similarity -- III: Approaches to Calculation I: Cohomology for Codimension One -- 1 Introduction -- 2 Inverse limit acceptance domains -- 3 Cohomology in the case d = N - 1 -- IV: Approaches to Calculation II: Infinitely Generated Cohomology -- 1 Introduction -- 2 The canonical projection tiling -- 3 Constructing C-topes -- 4 The indecomposable case -- 5 The decomposable case -- 6 Conditions for infinitely generated cohomology -- V: Approaches to Calculation III: Cohomology for Small Codimension -- 1 Introduction -- 2 Set up and statement of the results -- 3 Complexes defined by the singular spaces -- 4 Group homology -- 5 The spectral sequences -- 6 Example: Ammann-Kramer tilings -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.