Cohomology in one-dimensional substitution tiling spaces

DOI10.1090/S0002-9939-08-09225-3zbMath1139.37002arXivmath/0702669MaRDI QIDQ3506754

Beverly Diamond, Marcy M. Barge

Publication date: 17 June 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702669

zbMATH Keywords

inverse limitAnderson-Putnam complexcollaring tiles

Mathematics Subject Classification ID

Related Items (18)

Exact regularity and the cohomology of tiling spaces ⋮ An uncountable set of tiling spaces with distinct cohomology ⋮ Integer Cech cohomology of a class of n-dimensional substitutions ⋮ COHOMOLOGY OF THE PINWHEEL TILING ⋮ Small cocycles, fine torus fibrations, and a \({\mathbb {Z}^{2}}\) subshift with neither ⋮ On the structure of generic subshifts ⋮ The Cech cohomology and the spectrum for 1-dimensional tiling systems ⋮ Proximality and pure point spectrum for tiling dynamical systems ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ Self affine Delone sets and deviation phenomena ⋮ Beyond primitivity for one-dimensional substitution subshifts and tiling spaces ⋮ Geometric realization for substitution tilings ⋮ Homological Pisot substitutions and exact regularity ⋮ Relating diffraction and spectral data of aperiodic tilings: towards a Bloch theorem ⋮ Cohomology of substitution tiling spaces ⋮ Fusion: a general framework for hierarchical tilings of \(\mathbb{R }^d\) ⋮ On the $K$-theory of $C^*$-algebras associated to substitution tilings ⋮ Factors of Pisot tiling spaces and the Coincidence Rank Conjecture

Cites Work

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• Power of words and recognizability of fixpoints of a substitution
• Nonperiodicity implies unique composition for self-similar translationally finite tilings
• A characterization of substitutive sequences using return words
• A complete invariant for the topology of one-dimensional substitution tiling spaces
• Topological invariants for substitution tilings and their associated $C^\ast$-algebras

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