Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inner amenability, property Gamma, McDuff II_1 factors and stable
  equivalence relations   We say that a countable group $G$ is McDuff if it admits a free ergodic
probability measure preserving action such that the crossed product is a McDuff
II_1 factor. Similarly, $G$ is said to be stable if it admits such an action
with the orbit equivalence relation being stable. The McDuff property,
stability, inner amenability and property Gamma are subtly related and several
implications and non implications were obtained in
[Ef73,JS85,Va09,Ki12a,Ki12b]. We complete the picture with the remaining
implications and counterexamples.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat