On the Cohomology of Actions of Groups by Bernoulli Shifts

2003/10/15 by Sorin Popa, Popa, Sorin, Román Sasyk +2 · 9 citations
Mathematics · #28D05 #28D15 (Secondary) #46L10 (Primary) 22D40 #Action (physics) #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Bernoulli scheme #Bernoulli's principle #Character (mathematics) #Cohomology #Combinatorics #Countable set #Discrete mathematics #Equivariant cohomology #FOS: Mathematics #Geometry #Group (periodic table) #Group Theory (math.GR) #Linguistics #Mathematical Dynamics and Fractals #Mathematics #Operator Algebras (math.OA) #Physics #Property (philosophy) #Pure mathematics #Space (punctuation) #math.GR #math.OA #msc:22D40 #msc:28D05 #msc:28D15 #msc:46L10

paper · pdf · doi:10.48550/arxiv.math/0310211

published in arXiv (Cornell University) (Cornell University) · 9 pages; some corrections in Lemma 3.2 (Dec. 18, 2003), 10 pages

openalex publication_date 2003/10/15 · arxiv created 2003/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that if G is a countable, discrete group having infinite, normal subgroups with the relative property (T), then the Bernoulli shift action of G on \underset g ∈ G → Π (X₀, μ₀)_g for (X₀,μ₀) an arbitrary probability space, has first cohomology group isomorphic to the character group of G.

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• On Popa's Cocycle Superrigidity Theorem

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