Coût des relations d’équivalence et des groupes

By Damien Gaboriau. 2000

328 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c750e42821c85bb4c3f607f14d6417cc7ae27474

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Free Entropy (2001, background): “Another context involves measure-preserving equivalence relations, and a free probability interpretation [37] of the recent work on the cost of such equivalence relations [19].”
The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, methodology): “The costs of the mapping class groups of exceptional surfaces have already been calculated in [26].”
Some topics in the dynamics of group actions on rooted trees (2011, background): “As an interesting example of calculating a cost, note that the cost of the hereditary just-infinite group SL3(Z) is zero because this group has a system of generators in which each next term commutes with the preceding term and the orders of all generators are infinite [63].”
Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups (2006, background): “showing that the free groups Fn do not admit orbit equivalent essentially free ergodic actions for different values of n, see [18, 19].”
Borel Equivalence Relations (2010, background): “Moreoever the discussion of Borel equivalence relations is organized around the Borel reducibility order, ≤B, rather than notions such as orbit equivalence, as found in say [20], [18], [21], [53], [28], or notions of isomorphism, as discussed in [9].”
Expander graphs in pure and applied mathematics (2011, methodology): “course, it might be that both conjectures are false! One may even speculate that the xed price conjecture is false in general but it is true for hyperbolic groups, just as it is true for free groups ([Gab1]). If this is the case, or even if it is true for the much smaller class of fundamental groups”
A SURVEY OF MEASURED GROUP THEORY (2009, background): “So cocycle superrigidity theorems have an almost automatic bootstrap from lcsc groups to their lattices.”
Processes on Unimodular Random Networks (2006, background): “, to transient clusters of Bernoulli percolation; see Grimmett, Kesten, and Zhang (1993) and Benjamini, Lyons, and Schramm (1999) for sufficient conditions for transience.”