Some connections between coarse homotopy theory and shape theory

I introduce recent developments in coarse homotopy theory that build on prior results computing the coarse homotopy groups of cones over finite simplicial complexes cX, which coincide with the usual homotopy groups of the underlying space X (Mitchener, Norouzizadeh, Schick, 2020). Extending these ideas, I present new results on the coarse homotopy groups of cones over compact metric spaces. These are related to the Čech homotopy groups of the underlying space X via a ${\underleftarrow{\lim }}^1$ sequence. In this talk, I will provide a brief outline of the proof, present some interesting examples, and discuss the implications of this work in bridging coarse homotopy theory and shape theory.