Topological Entropy and the Variational Principle for Actions of Sofic Groups

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants. We establish the variational principle in this sofic context and use it to compute the topological entropy of certain algebraic actions of residually finite groups.