Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact actions and uniqueness of the group measure space decomposition
  of II$_1$ factors   We prove that any II$_1$ factor $L^{\infty}(X)\rtimes\Gamma$ arising from a
compact, free, ergodic, probability measure preserving action of a countable
group $\Gamma$ with positive first $\ell^2$-Betti number, has a unique group
measure space Cartan subalgebra, up to unitary conjugacy.

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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio