Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological dynamical systems associated to II_1 factors   If $N \subset \R$ is a separable II$_1$-factor, the space $\Hom(N,\R)$ of
unitary equivalence classes of unital *-homomorphisms $N \to \R$ is shown to
have a surprisingly rich structure. If $N$ is not hyperfinite, $\Hom(N,\R)$ is
an infinite-dimensional, complete, metrizeable topological space with
convex-like structure, and the outer automorphism group $\Out(N)$ acts on it by
"affine" homeomorphisms. (If $N \cong R$, then $\Hom(N,\R)$ is just a point.)
Property (T) is reflected in the extreme points -- they're discrete in this
case. For certain free products $N = \Sigma \ast R$, every countable group acts
nontrivially on $\Hom(N, \R)$, and we show the extreme points are not discrete
for these examples. Finally, we prove that the dynamical systems associated to
free group factors are isomorphic.

14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph