The Ruelle-Sullivan map for actions of \(\mathbb R^n\)

DOI10.1007/s00208-005-0728-1zbMath1098.37004OpenAlexW2047331334MaRDI QIDQ818569

Johannes Kellendonk, Ian F. Putnam

Publication date: 21 March 2006

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-005-0728-1

zbMATH Keywords

Čech cohomologycurrentsDelone setsactions of cohomology groupsRuelle-Sullivan map

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Topological transformation groups (57S99) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Homology and cohomology theories in algebraic topology (55N99) Boundary regularity of mappings in several complex variables (32H40) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (30)

Exact regularity and the cohomology of tiling spaces ⋮ Bragg spectrum, K-theory, and gap labeling of aperiodic solids ⋮ Pattern-equivariant homology ⋮ A spectral sequence for theK-theory of tiling spaces ⋮ Small cocycles, fine torus fibrations, and a \({\mathbb {Z}^{2}}\) subshift with neither ⋮ Complexity as a homeomorphism invariant for tiling spaces ⋮ The Cech cohomology and the spectrum for 1-dimensional tiling systems ⋮ Pattern equivariant functions, deformations and equivalence of tiling spaces ⋮ Randomness and topological invariants in pentagonal tiling spaces ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ The mapping class group of a minimal subshift ⋮ 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 ⋮ Rokhlin dimension for flows ⋮ Homological Pisot substitutions and exact regularity ⋮ \(K\)-theory of crossed products of tiling \(C^*\)-algebras by rotation groups ⋮ Pattern-equivariant cohomology with integer coefficients ⋮ Comparing different versions of tiling cohomology ⋮ Traces of random operators associated with self-affine Delone sets and Shubin's formula ⋮ Random substitution tilings and deviation phenomena ⋮ Relating diffraction and spectral data of aperiodic tilings: towards a Bloch theorem ⋮ Aperiodicity, rotational tiling spaces and topological space groups ⋮ Rotation numbers and rotation classes on one-dimensional tiling spaces ⋮ Substitutions with vanishing rotationally invariant first cohomology ⋮ Equilibrium configurations for generalized Frenkel-Kontorova models on quasicrystals ⋮ On the $K$-theory of $C^*$-algebras associated to substitution tilings ⋮ Statistical properties of Lorentz gases on aperiodic tilings, Part 1 ⋮ Simple dimension groups that are isomorphic to stationary inductive limits

Cites Work

• Proximal flows
• Pointwise theorems for amenable groups.
• Topological invariants for projection method patterns
• The cohomology and $K$-theory of commuting homeomorphisms of the Cantor set
• Pattern-equivariant functions and cohomology
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