On Sofic Actions and Equivalence Relations

By Liviu Paunescu. 2010

61 citations recorded by the source corpus.

The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes' embedding problem, and prove the equivalence of this two definitions. We introduce a notion of sofic action for an arbitrary group and prove that amalgamated product of sofic actions over amenable groups is again sofic. We also prove that amalgamated product of sofic groups over an amenable subgroup is again sofic.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fec5b08a1302c1f5e4dfa33e5024c02f0b1c4928

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In Geometry and Topology

1. Ben Hayes
2. Valerio Capraro
3. Martino Lupini
4. William Slofstra

In Mathematical Physics

1. Ben Hayes
2. Valerio Capraro
3. Martino Lupini
4. William Slofstra

In Statistics and Probability

1. Ben Hayes
2. Valerio Capraro
3. Martino Lupini

Citations in the corpus

• Fuglede–Kadison Determinants and Sofic Entropy (2014, background): “The class of sofic groups contains all amenable groups, all residually finite groups, all linear groups and is closed under direct unions and free products with amalgamation over amenable subgroups (see [16],[14],[36],[38]).”
• Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “The fact that free product of sofic groups amalgamated over an amenable groups is sofic has been shown in [29] in the particular case of amenable monotileable groups and in [40] and [95] in full generality.”