Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

The Whitehead type theorems in coarse shape theory

Pages: 103 – 125

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a6

Authors

Nikola Koceić Bilan (Department of Mathematics, University of Split, Croatia)

Nikica Uglešić (University of Zadar, Croatia)

Abstract

The analogues of Whitehead’s theorem in coarse shape theory, i.e., in the pointed coarse pro-category pro*-$\mathrm{HPol}_0$ and in the pointed coarse shape category $Sh^*_0$, are proved. In other words, if a pointed coarse shape morphism of finite shape dimensional spaces induces isomorphisms (epimorphism, in the top dimension) of the corresponding coarse $k$-dimensional homotopy pro-groups, then it is a pointed coarse shape isomorphism.

Keywords

inverse system, pro-category, pro*-category, expansion, shape, coarse shape, homotopy pro-group, $m$-equivalence

2010 Mathematics Subject Classification

55N99, 55P55, 55Q05

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