Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On dense totipotent free subgroups in full groups   We study probability measure preserving (p.m.p.) non-free actions of free
groups and the associated IRS's. The perfect kernel of a countable group Gamma
is the largest closed subspace of the space of subgroups of Gamma without
isolated points. We introduce the class of totipotent ergodic p.m.p. actions of
Gamma: those for which almost every point-stabilizer has dense conjugacy class
in the perfect kernel. Equivalently, the support of the associated IRS is as
large as possible, namely it is equal to the whole perfect kernel. We prove
that every ergodic p.m.p. equivalence relation R of cost $<r$ can be realized
by the orbits of an action of the free group F_r on r generators that is
totipotent and such that the image in the full group [R] is dense. We explain
why these actions have no minimal models.This also provides a continuum of
pairwise orbit inequivalent invariant random subgroups of F_r, all of whose
supports are equal to the whole space of infinite index subgroups. We are led
to introduce a property of topologically generating pairs for full groups (we
call evanescence) and establish a genericity result about their existence. We
show that their existence characterizes cost 1.

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The categories of this paper are: nlin
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc