Equivariant persistence topological complexity

We introduce equivariant persistent analogues of Lusternik-Schnirelmann category, topological complexity, cup length, and zero-divisors cup length for persistent spaces with group actions, and establish their stability. In particular, we investigate their behavior under equivariant interleavings and obtain bounds for the corresponding erosion distances. For Vietoris–Rips filtrations of compact metric spaces equipped with compatible group actions, we relate the erosion distances between the resulting equivariant persistent invariants to appropriate equivariant versions of the Gromov-Hausdorff distance.