Tiling spaces are inverse limits

DOI10.1063/1.1613041zbMath1063.37019arXivmath/0210179OpenAlexW2019510582MaRDI QIDQ4833188

Lorenzo Sadun

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210179

Mathematics Subject Classification ID

Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items

Minimal configurations for the Frenkel-Kontorova model on a quasicrystal, COHOMOLOGY OF THE PINWHEEL TILING, A spectral sequence for theK-theory of tiling spaces, Tiling groupoids and Bratteli diagrams, Pattern equivariant functions, deformations and equivalence of tiling spaces, Classifying matchbox manifolds, Self affine Delone sets and deviation phenomena, Complexity and cohomology for cut-and-projection tilings, A primer of substitution tilings of the Euclidean plane, Conjugacies of model sets, Shape of matchbox manifolds, Pattern-equivariant cohomology with integer coefficients, Comparing different versions of tiling cohomology, Substitution tilings with statistical circular symmetry, Fusion: a general framework for hierarchical tilings of \(\mathbb{R }^d\), Spectral continuity for aperiodic quantum systems: Applications of a folklore theorem, Self-similar tilings of fractal blow-ups, Rotation topological factors of minimal $\mathbb {Z}^{d}$-actions on the Cantor set

Cites Work

• The pinwheel tilings of the plane
• A homeomorphism invariant for substitution tiling spaces
• Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
• Topological invariants for substitution tilings and their associated $C^\ast$-algebras
• Tiling spaces are Cantor set fiber bundles
• On the dynamics of \mathbb{G} -solenoids. Applications to Delone sets
• NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING