Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Co-induction and Invariant Random Subgroups   In this paper we develop a co-induction operation which transforms an
invariant random subgroup of a group into an invariant random subgroup of a
larger group.
  We use this operation to construct new continuum size families of non-atomic,
weakly mixing invariant random subgroups of certain classes of wreath products,
HNN-extensions and free products with amalgamation. By use of small
cancellation theory, we also construct a new continuum size family of
non-atomic invariant random subgroups of $\mathbb{F}_2$ which are all invariant
and weakly mixing with respect to the action of $\text{Aut}(\mathbb{F}_2)$.
  Moreover, for amenable groups $\Gamma\leq \Delta$, we obtain that the
standard co-induction operation from the space of weak equivalence classes of
$\Gamma$ to the space of weak equivalence classes of $\Delta$ is continuous if
and only if $[\Delta :\Gamma]<\infty$ or $\text{core}_\Delta(\Gamma)$ is
trivial. For general groups we obtain that the co-induction operation is not
continuous when $[\Delta:\Gamma]=\infty$. This answers a question raised by
Burton and Kechris. Independently such an answer was also obtained, using a
different method, by Bernshteyn.

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The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci