Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On rigid stabilizers and invariant random subgroups of groups of
  homeomorphisms   A generalization of the double commutator lemma for normal subgroups is shown
for invariant random subgroups of a countable group acting faithfully on a
Hausdorff space. As an application, we classify ergodic invariant random
subgroups of topological full groups of Cantor minimal
$\mathbb{Z}^{d}$-systems. Another corollary is that for an ergodic invariant
random subgroup of a branch group, a.e. subgroup $H$ must contain derived
subgroups of certain rigid stabilizers. Such results can be applied towards
classification of invariant random subgroups of Grigorchuk groups.

20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin