Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Piecewise strongly proximal actions, free boundaries and the Neretin
  groups   A closed subgroup $H$ of a locally compact group $G$ is confined if the
closure of the conjugacy class of $H$ in the Chabauty space of $G$ does not
contain the trivial subgroup. We establish a dynamical criterion on the action
of a totally disconnected locally compact group $G$ on a compact space $X$
ensuring that no relatively amenable subgroup of $G$ can be confined. This
property is equivalent to the fact that the action of $G$ on its Furstenberg
boundary is free. Our criterion applies to the Neretin groups. We deduce that
each Neretin group has two inequivalent irreducible unitary representations
that are weakly equivalent. This implies that the Neretin groups are not of
type I, thereby answering a question of Y.~Neretin.

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The categories of this paper are: stat
12
The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom