Convex Structures Revisited

We provide a complete characterisation of extreme points of the space of sofic representations. We also show that the restriction map $Sof(G,P^{\omega })$ to $Sof(H,P^{\omega })$, where $H\subset G$ is not always surjective. The first part of the paper is a continuation of [Pa2] and follows more closely the plan of Nathanial Brown from [Br].