Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commensurated subgroups and micro-supported actions   Let $\Gamma$ be a finitely generated group and $X$ be a minimal compact
$\Gamma$-space. We assume that the $\Gamma$-action is micro-supported, i.e. for
every non-empty open subset $U \subseteq X$, there is an element of $\Gamma$
acting non-trivially on $U$ and trivially on the complement $X \setminus U$. We
show that, under suitable assumptions, the existence of certain commensurated
subgroups in $\Gamma$ yields strong restrictions on the dynamics of the
$\Gamma$-action: the space $X$ has compressible open subsets, and it is an
almost $\Gamma$-boundary. Those properties yield in turn restrictions on the
structure of $\Gamma$: $\Gamma$ is neither amenable nor residually finite.
Among the applications, we show that the (alternating subgroup of the)
topological full group associated to a minimal and expansive Cantor action of a
finitely generated amenable group has no commensurated subgroups other than the
trivial ones. Similarly, every commensurated subgroup of a finitely generated
branch group is commensurate to a normal subgroup; the latter assertion relies
on an appendix by Dominik Francoeur, and generalizes a result of Phillip
Wesolek on finitely generated just-infinite branch groups. Other applications
concern discrete groups acting on the circle, and the centralizer lattice of
non-discrete totally disconnected locally compact (tdlc) groups. Our results
rely, in an essential way, on recent results on the structure of tdlc groups,
on the dynamics of their micro-supported actions, and on the notion of
uniformly recurrent subgroups.

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The categories of this paper are: eess
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The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th