Andrew Dykstra (University of Maryland)

Good almost conjugacy for G-shifts of finite type

Abstract. Let $G$ be a finite group. A $G$ -shift of finite type ($G$ -SFT) is an SFT equipped with a continuous shift-commuting G action. Answering a question of Parry, we classify irreducible G-SFTs up to right-closing almost conjugacy (RCAC). In particular, for mixing G-shifts of finite type where the $G$ action is free, TFAE:

1. entropy and ideal class agree,
2. the $G$ -SFTs are right closing almost conjugate as SFTs,
3. the $G$ -SFTs are right closing almost conjugate.

In the general irreducible case, period and one additional invariant are also needed for the classification. The equivalence relation RCAC is of interest because of its connects with algebraic invariants, resolving maps and the measurable relation of regular isomorphism. This talk is based on ``Right closing almost conjugacy for G-shifts of finite type"; a preprint is available on my webpage (Google: Andrew Dykstra).