A Survey on Connes' Embedding Conjecture

Abstract

In a very celebrated paper A. Connes has formulated a conjecture which is now one of the most important open problem in Operator Algebras. This importance comes from the works of many mathematicians who have found some unexpected equivalent statements showing as this conjecture is transversal to almost all the sub-specialization of Operator Algebras. In this survey I would like to give a more or less detailed description of all these approaches.