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 Polish groups which admit two-sided invariant metric (TSI). Since abelian are TSI, unbalancedness can be used for identifying classification problems cannot solved classical homology and cohomology theories. terms applications, show that Morita continuous-trace C ? C^* -algebras, as well isomorphism Hermitian line bundles, not classifiable TSI groups. process, Wreath product any two non-compact subgroups S Subscript normal infinity"> S ? encoding="application/x-tex">S_{\infty } admits an action whose relation is generically ergodic against group deduce there CLI