Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical obstructions to classification by (co)homology and other
  TSI-group invariants   In the spirit of Hjorth's turbulence theory, we introduce "unbalancedness": a
new dynamical obstruction to classifying orbit equivalence relations by actions
of Polish groups which admit a two side invariant metric (TSI). Since abelian
groups are TSI, unbalancedness can be used for identifying which classification
problems cannot be solved by classical homology and cohomology theories.
  In terms of applications, we show that Morita equivalence of continuous-trace
$C^*$-algebras, as well as isomorphism of Hermitian line bundles, are not
classifiable by actions of TSI groups. In the process, we show that the Wreath
product of any two non-compact subgroups of $S_{\infty}$ admits an action whose
orbit equivalence relation is generically ergodic against any action of a TSI
group and we deduce that there is an orbit equivalence relation of a CLI group
which is not classifiable by actions of TSI groups.

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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg