Topological pressure and the variational principle for actions of sofic groups

TL;DR

This paper extends the concept of topological pressure to actions of sofic groups on compact spaces and proves a variational principle, broadening the scope from amenable groups to sofic groups.

Contribution

It introduces topological pressure for sofic group actions and establishes the variational principle in this more general setting.

Findings

Generalizes topological pressure to sofic group actions

Proves the variational principle for these actions

Bridges classical theory with sofic group dynamics

Abstract

In this paper, we introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure for continuous actions of countable amenable groups on such spaces. We also establish the variational principle for topological pressure in this sofic context.