Global Aspects of Ergodic Group Actions

By Alexander S. Kechris. 2010

255 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f7f22ded5189c345b59a7b6f5cec903327c2185d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Metrizable universal minimal flows of Polish groups have a comeagre orbit (2016, unknown): “(See, for example, [Kec 10 , Chapter I, 3 ] for the deﬁnition and their basic properties.)”
The Haagerup property for locally compact quantum groups (2013, methodology): “ the set of all unitary representations of Gon a ﬁxed inﬁnite-dimensional, separable Hilbert space Hwith a natural Polish topology (for the analogous concepts in the classical framework, see the book [Kec]) and give conditions for density of classes of representations. Fix an inﬁnite-dimensional sep”
Ultraproducts of measure preserving actions and graph combinatorics (2012, background): “1 in Kechris [Ke2] shows that for n ∈ U there is bn ∼= an with bn ∈ V .”
Invariant random subgroups of the free group (2012, methodology): “ility space, E⊂ X× Xa discrete Borel equivalence relation such that µis E-invariant. We will usually assume that Eis ergodic and aperiodic (which means that a.e. equivalence class is inﬁnite). We use [Ke10] as a general reference. Let Aut(X,µ) be the group of measure-preserving automorphisms of (X,µ”
Limits of locally–globally convergent graph sequences (2012, background): “We say that and G 2 are locally-globally equivalent if and only if both In the setting of group actions, this partial order means the same as “weak containment” of the corresponding group actions, and local-global equivalence corresponds to “weak equivalence” (Kechris [21]).”
ORBIT INEQUIVALENT ACTIONS OF NON-AMENABLE GROUPS (2007, background): “I would also like to thank Alexander Kechris for providing excellent notes and comments concerning the proof I present here.”
Orbit Equivalence and Measured Group Theory (2010, background): “In his very rich monograph [Kec10], Kechris studied the continuity properties of the cost function on the space of actions and proved that Cost(R) > 1 for an ergodic R forces its outer automorphism group to be Polish.”