Tangential equivalence of group actions

Equivalence Relations Invariant under Group Actions

We study, in an abstract context, equivalence relations which are invariant under group actions. More precisely, we fix a transformation group, and we study the orbital equivalence relations (i.e. orbit equivalence relations of normal subgroups) and a wider class of weakly orbital equivalence relations. For these sorts of relations we show (under some additional assumptions) that if each class ...

Equivalence of Nearby Differentiable Actions of a Compact Group

In this note we will be concerned with the proof and consequences of the following fact : if o is a differentiate action of a compact Lie group on a compact differentiate manifold M, then any differentia t e action of G on M sufficiently close to 0o in the C^topology is equivalent to 0O. 1. Notation. In what follows differentiate means class C. If M and V are differentiate manifolds, 2HI(M, ...

On Morita Equivalence of Group Actions on Locally C-algebras

In this paper, we prove that two continuous inverse limit actions α and β of a locally compact group G on the locally C-algebras A and B are strongly Morita equivalent if and only if there is a locally C-algebra C such that A and B appear as two complementary full corners of C and there is a continuous action γ of G on C which leaves A and B invariant such that γ|A = α and γ|B = β. This general...

Conjugacy, orbit equivalence and classification of measure preserving group actions

We prove that if G is a countable discrete group with property (T) over an infinite subgroup H < G which contains an infinite Abelian subgroup or is normal, then G has continuum many orbit inequivalent measure preserving a.e. free ergodic actions on a standard Borel probability space. Further, we obtain that the measure preserving a.e. free ergodic actions of such a G cannot be classified up to...

Global Aspects of Ergodic Group Actions and Equivalence Relations