Continuity of coarse shape groups

We show that every coarse shape group can be obtained as the inverse limit of an inverse system of the groups coming from an $\mathrm{HPol}_{\star}$-expansion. This provides a way of computing of these interesting topological invariants (whose algebraic structure is significantly richer than those of the homotopy and shape groups) in an easier manner. It is proven that, for inverse systems of compact polyhedra, the coarse shape group functor commutes with the inverse limit.

Keywords

inverse limit, inverse system, pro-category, pro$^{\ast}$-category, expansion, shape, coarse shape, homotopy (pro-)group, coarse shape group

2010 Mathematics Subject Classification

55N99, 55P55, 55Q05

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Published 29 November 2016