ON THE VANISHING COHOMOLOGY PROBLEM FOR COCYCLE ACTIONS OF GROUPS ON II_1 FACTORS

SORIN POPA

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ON THE VANISHING COHOMOLOGY PROBLEM FOR COCYCLE ACTIONS OF GROUPS ON II_1 FACTORS

机译：关于II_1因素群体群体作用的消失协调问题

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We prove that any free cocycle action of a countable amenable group Γ on any II_1 factor N can be perturbed by inner automorphisms to a genuine action. Besides being satisfied by all amenable groups, this universal vanishing cohomology property, that we call VC, is also closed to free products with amalgamation over finite groups. While no other examples of VC-groups are known, by considering special cocycle actions Γ → N in the case N is the hyperfinite II_1 factor R, respectively the free group factor N = L(F_∞), we exclude many groups from being VC. We also show that any free action Γ → R gives rise to a free cocycle Γ-action on the II_1 factor R' ∩ R~ω whose vanishing cohomology is equivalent to Connes' Approximate Embedding property for the II_1 factor R ? Γ.

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《Annales scientifiques de l'Ecole normale superieure》 |2021年第2期|共37页
作者
SORIN POPA;
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作者单位

Math.Dept. UCLA Los Angeles CA 90095-1555 USA;

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原文格式 PDF
正文语种 eng
中图分类自然科学总论;师范教育理论;
关键词
VANISHING; PROBLEM; FACTORS;

机译：消失;问题;因素;

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ON THE VANISHING COHOMOLOGY PROBLEM FOR COCYCLE ACTIONS OF GROUPS ON II_1 FACTORS

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