Pattern equivariant functions, deformations and equivalence of tiling spaces

DOI10.1017/S014338570700065XzbMath1149.52017arXivmath/0703156MaRDI QIDQ3528756

Johannes Kellendonk

Publication date: 17 October 2008

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703156

Mathematics Subject Classification ID

Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items (18)

Rigidity and mapping class group for abstract tiling spaces ⋮ Finitely balanced sequences and plasticity of 1-dimensional tilings ⋮ Quasimusic: tilings and metre ⋮ Pattern-equivariant homology ⋮ Small cocycles, fine torus fibrations, and a \({\mathbb {Z}^{2}}\) subshift with neither ⋮ Complexity as a homeomorphism invariant for tiling spaces ⋮ Delone dynamical systems and spectral convergence ⋮ Gabor frames for quasicrystals, \(K\)-theory, and twisted gap labeling ⋮ Integral cohomology of rational projection method patterns ⋮ Operators, Algebras and Their Invariants for Aperiodic Tilings ⋮ Self affine Delone sets and deviation phenomena ⋮ The cohomological equation over dynamical systems arising from Delone sets ⋮ Tiling deformations, cohomology, and orbit equivalence of tiling spaces ⋮ Conjugacies of model sets ⋮ Pattern equivariant cohomology and theorems of Kesten and Oren ⋮ Comparing different versions of tiling cohomology ⋮ Spectral continuity for aperiodic quantum systems I. General theory ⋮ Statistical properties of Lorentz gases on aperiodic tilings, Part 1

Cites Work

• The Ruelle-Sullivan map for actions of \(\mathbb R^n\)
• When shape matters: deformations of tiling spaces
• Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
• Topological equivalence of tilings
• Tiling spaces are Cantor set fiber bundles
• Pattern-equivariant functions and cohomology
• Tiling spaces are inverse limits
• Pattern-equivariant cohomology with integer coefficients

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