engleski

Computing of the coarse shape groups

The coarse shape groups are new topological invariants which are (coarse) shape and homotopy invariants, as well. Their structure is signi…cantly richer than the structure of shape groups. They provide information (especially, about compacta) even better than the homo- topy pro-groups. Since nontrivial coarse shape groups, even for poly- hedra, are too large, it is di¢ cult to calculate them exactly. In this talk, we give an explicit formula for computing coarse shape groups of a large class of metric compacta including solenoids. Moreover, we show that every coarse shape group can be obtained as the inverse limit of an inverse system of groups. It is proven that, for inverse systems of compact polyhedra, the coarse shape group functor commutes with the inverse limit. These results provide computing of coarse shape groups in an easier manner.

coarse shape coarse shape group; homotopy pro-groups

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