Topics in orbit equivalence

By Alexander S. Kechris. 2004

333 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5af37283cafa2923327615faa00aeb9cfd77e295

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Andrew S. Marks
2. A. Furman
3. Inessa Epstein
4. Russell Lyons
5. Nikolay Nikolov
6. Damien Gaboriau
7. L. Lov'asz
8. Gábor Elek

In Geometry and Topology

1. A. Furman
2. Damien Gaboriau
3. Y. Kida
4. Alexander S. Kechris
5. Adrian Ioana
6. Russell Lyons
7. Alexander Lubotzky
8. David Kerr

Citations in the corpus

• A nonamenable finitely presented group of piecewise projective homeomorphisms (2016, background): “Finally, Section 5 contains a proof that the relations isolated in Section 3 su ce to give a presentation for ha; b; ci.”
• Soficity, amenability, and dynamical entropy (2010, background): “Since G is finite, we can find a measurable subset Y of X such that | Y ∩ Gx | = 1 for every x ∈ X [8, Ex.”
• The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, background): “We recommend the reader to consult [26], [54] for more details about cost.”
• Processes on Unimodular Random Networks (2006, background): “able by Kaimanovich (1997), and hence hyperfinite by a theorem of Connes, Feldman, and Weiss (1981). (Another proof of the latter theorem was sketched by Kaimanovich (1997), with more details given by Kechris and Miller (2004)). Translating the definition of hyperfinite equivalence relation to rooted n”
• ORBIT INEQUIVALENT ACTIONS OF NON-AMENABLE GROUPS (2007, methodology): “Consider the ergodic decomposition of Y with respect to the action Γ y Y (see Kechris-Miller [KM]).”
• Borel Equivalence Relations (2010, background): “The reader might also look at [5] for a closer examination of some of the issues surrounding actions induced by Polish group actions, or at [31] for a discussion of the Vaught conjecture, or [48] for orbit equivalence.”
• Stability and invariant random subgroups (2018, background): “For a thorough treatment of Borel equivalence relations, see [15].”
• Global Aspects of Ergodic Group Actions (2010, methodology): “General references for this theory are Gaboriau [Ga1] and Kechris-Miller [KM].”
• A measurable-group-theoretic solution to von Neumann’s problem (2007, background): “28]). Otherwise, one first considers the restriction of the treeable S1 to a small enough Borel subset V : this increases the normalized cost by the induction formula of [3, Proposition II.6 (2)] to get C(S1| V) ≥ 2. In fact, it follows from the proof of [ 7, Theorem 28.3 ] that a treeable probabili”
• Large Networks and Graph Limits (2012, background): “, φk) will be called a measure preserving family (see Gaboriau [2002], Kechris and Miller [2004]).”
• Rank gradient, cost of groups and the rank versus Heegaard genus problem (2007, methodology): “The analytic notion of cost was introduced by Levitt [18] and used by Gaboriau [11] to show that free groups of different rank do not admit orbit equivalent measurable actions (see also the book of Kechris and Miller [15]).”