TY  - BOOK
AU  - Forrest,Alan
AU  - Hunton,John
AU  - Kellendonk,Johannes
TI  - Topological Invariants for Projection Method Patterns
T2  - Memoirs of the American Mathematical Society
SN  - 9781470403515
AV  - QA640.72 -- .F67 2002eb 
U1  - 510 s;516 
PY  - 2002///
CY  - Providence
PB  - American Mathematical Society
KW  - Aperiodic tilings
KW  - Invariants
KW  - K-theory
KW  - Topological dynamics
KW  - Electronic books
N1  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114457
ER  -