In this talk, we introduce the notion of equivariant homotopic distance between G-maps. This invariant provides a unified framework that includes the equivariant Lusternik–Schnirelmann category and equivariant topological complexity as particular cases, and it is also closely related to the equivariant sectional category.
We discuss its basic properties, including homotopy invariance and a triangle inequality in the equivariant setting. We also present cohomological and dimension–connectivity bounds, along with some structural applications to Hopf G-spaces.
