On exactness of the coarse shape group sequence (Q2901999)

Coarse shape which is neither identical with ordinary shape nor with the homotopy category of based or unbased pairs of topological spaces was recently established by the present author and N. Uglešić. Unlike all other definitions of shape it does not agree with the homotopy category of spaces for \textit{good} (i.e., polyhedral) spaces. The main objective of the present paper is the introduction of relative \textit{coarse shape homotopy groups} \(\check{\pi}^\star_k (X,X_0,x_0)\). They allow a long exact homotopy sequence other than the ordinary shape homotopy groups.