Pattern-equivariant cohomology with integer coefficients

DOI10.1017/S0143385707000259zbMath1127.37006arXivmath/0602066MaRDI QIDQ5436461

Lorenzo Sadun

Publication date: 16 January 2008

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

Full work available at URL: https://arxiv.org/abs/math/0602066

zbMATH Keywords

Čech cohomology of the tiling spacePE cohomologyPE representation variety

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Topological dynamics (37B99) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)

Related Items

Exact regularity and the cohomology of tiling spaces, An uncountable set of tiling spaces with distinct cohomology, Finitely balanced sequences and plasticity of 1-dimensional tilings, Pattern-equivariant homology, Small cocycles, fine torus fibrations, and a \({\mathbb {Z}^{2}}\) subshift with neither, Pattern equivariant functions, deformations and equivalence of tiling spaces, Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017, Self affine Delone sets and deviation phenomena, Conjugacies of model sets, Homological Pisot substitutions and exact regularity, Pattern equivariant cohomology and theorems of Kesten and Oren, Comparing different versions of tiling cohomology, Random substitution tilings and deviation phenomena, Aperiodicity, rotational tiling spaces and topological space groups, Rotation numbers and rotation classes on one-dimensional tiling spaces, On the $K$-theory of $C^*$-algebras associated to substitution tilings

Cites Work

• The Ruelle-Sullivan map for actions of \(\mathbb R^n\)
• Spaces of tilings, finite telescopic approximations and gap-labeling
• Towards a characterization of self-similar tilings in terms of derived Voronoï tessellations
• A homeomorphism invariant for substitution tiling spaces
• Tilings, fundamental cocycles and fundamental groups of symbolic ${\Bbb Z}^{d}$-actions
• Topological invariants for substitution tilings and their associated $C^\ast$-algebras
• Pattern-equivariant functions and cohomology
• On the dynamics of \mathbb{G} -solenoids. Applications to Delone sets
• Tiling spaces are inverse limits
• The projective fundamental group of a ℤ²-shift
• Expanding attractors