Sofic equivalence relations

By Gábor Elek, Gábor Lippner. 2009

57 citations recorded by the source corpus.

We introduce the notion of sofic measurable equivalence relations. Using them we prove that Connes' Embedding Conjecture as well as the Measurable Determinant Conjecture of Luck, Sauer and Wegner hold for treeable equivalence relations.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/607608b170d7f51ca6acb346cb6e4be09eaf5862

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. Omer Angel
2. Russell Lyons
3. Oded Schramm
4. Asaf Nachmias
5. Itai Benjamini
6. Gourab Ray
7. Tom Hutchcroft
8. Ben Hayes

In Geometry and Topology

1. Russell Lyons
2. Asaf Nachmias
3. Omer Angel
4. Gourab Ray
5. Tom Hutchcroft
6. Damien Gaboriau
7. Ben Hayes
8. Itai Benjamini

In Mathematical Physics

1. Russell Lyons
2. Omer Angel
3. Asaf Nachmias
4. Itai Benjamini
5. Oded Schramm
6. Gourab Ray
7. Tom Hutchcroft
8. Nicolas Curien

Citations in the corpus

• Unimodular random trees (2012, methodology): “As noted by Elek and Lippner [15], this implies that every treeable group is sofic.”
• Hyperbolic and Parabolic Unimodular Random Maps (2016, methodology): “The following theorem is an adaptation of a related theorem of Elek and Lippner [33] in the setting of group actions.”
• Orbit Equivalence and Measured Group Theory (2010, background): “It is satisfied by profinite actions, treeable equivalence relations and Bernoulli shifts of sofic groups [EL10].”
• Fuglede–Kadison Determinants and Sofic Entropy (2014, background): “We need the following result of Elek-Lippner (see [15] Theorem 3 in Section 6), which follows from the weak∗ convergence we have already shown.”