Sofic dimension for discrete measured groupoids

DOI10.1090/S0002-9947-2013-05987-9zbMath1352.20039arXiv1111.2842MaRDI QIDQ5402108

David Kerr, Mikaël Pichot, Kenneth J. Dykema

Publication date: 5 March 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.2842

Mathematics Subject Classification ID

Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Topological groupoids (including differentiable and Lie groupoids) (22A22) Means on groups, semigroups, etc.; amenable groups (43A07) General groups of measure-preserving transformations and dynamical systems (37A15) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05)

Related Items (17)

Fuglede-Kadison determinants and sofic entropy ⋮ Metric Approximations of Wreath Products ⋮ On sofic groupoids and their full groups ⋮ The relative f-invariant and non-uniform random sofic approximations ⋮ Metric mean dimension for algebraic actions of Sofic groups ⋮ Sofic entropy of Gaussian actions ⋮ Locally compact sofic groups ⋮ POLISH MODELS AND SOFIC ENTROPY ⋮ Sofic boundaries of groups and coarse geometry of sofic approximations ⋮ An \(l^p\)-version of von Neumann dimension for Banach space representations of sofic groups. II ⋮ Sofic dimension for discrete measured groupoids ⋮ Max-min theorems for weak containment, square summable homoclinic points, and completely positive entropy ⋮ Soficity, short cycles, and the Higman group ⋮ Relative entropy and the Pinsker product formula for sofic groups ⋮ Entropy theory for sofic groupoids. I: The foundations ⋮ Examples in the entropy theory of countable group actions ⋮ On sofic monoids

Cites Work

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• Sofic measure entropy via finite partitions
• On sofic actions and equivalence relations
• Entropy and the variational principle for actions of sofic groups
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• Entropy and isomorphism theorems for actions of amenable groups
• Microstates free entropy and cost of equivalence relations
• Cost of equivalence relations and groups
• Soficity, amenability, and dynamical entropy
• Free products of sofic groups with amalgamation over monotileably amenable groups
• Sofic representations of amenable groups
• L²-BETTI NUMBERS OF DISCRETE MEASURED GROUPOIDS
• Free entropy dimension in amalgamated free products
• Measure conjugacy invariants for actions of countable sofic groups
• A Topological Application of the Isoperimetric Inequality
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
• The free entropy dimension of hyperfinite von Neumann algebras
• Sofic dimension for discrete measured groupoids

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