\(\mathbb{Z}^d\)-odometers and cohomology

DOI10.4171/GGD/509zbMath1432.37013arXiv1709.08585OpenAlexW3101020189MaRDI QIDQ2327664

Ian F. Putnam, Christian F. Skau, Thierry Giordano

Publication date: 15 October 2019

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.08585

zbMATH Keywords

dynamical systemscohomologyorbit equivalenceodometers

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (11)

Generalized ideal classes in application to toroidal solenoids ⋮ Rank-two solenoidal endomorphisms ⋮ Prime spectrum and dynamics for nilpotent Cantor actions ⋮ Low-dimensional solenoidal manifolds ⋮ Continuous orbit equivalence rigidity for left-right wreath product actions ⋮ Nilpotent Cantor actions ⋮ Arboreal Cantor actions ⋮ Limit group invariants for non-free Cantor actions ⋮ Cantor dynamics of renormalizable groups ⋮ Model-theoretic properties of dynamics on the Cantor set ⋮ Topological speedups of ℤ^d-actions

Cites Work

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• \(\mathbb Z^d\) Toeplitz arrays
• Orbit equivalence for Cantor minimal \(\mathbb Z^d\)-systems
• Orbit equivalence rigidity of equicontinuous systems
• Topological invariants for projection method patterns
• G -odometers and their almost one-to-one extensions
• COCYCLES FOR CANTOR MINIMAL ℤ^d-SYSTEMS
• The cohomology and $K$-theory of commuting homeomorphisms of the Cantor set
• Continuous orbit equivalence rigidity
• Abelian Groups

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