Computing coarse shape groups of solenoids

Abstract

The coarse shape groups are new topological invariants which are (coarse) shape and homotopy invariants as well. Their structure is significantly richer than the structure of shape groups. They provide information (especially, about compacta) even better than the homotopy $pro$-groups. Since nontrivial coarse shape groups, even for polyhedra, are too large, it is difficult to calculate them exactly. Herein, we give an explicit formula for computing coarse shape groups of a large class of metric compacta including solenoids.