Extension of maps to nilpotent spaces. II

https://doi.org/10.1016/S0166-8641(01)00239-5Get rights and content
Under an Elsevier user license
open archive

Abstract

Let M be a nilpotent CW-complex with finitely generated fundamental group. We give necessary and sufficient cohomological dimension theory conditions for a finite-dimensional metric compactum X so that every map AM, where A is a closed subset of X can be extended to a map XM.

This is a generalization of a result by Dranishnikov [Mat. Sb. 182 (1991)] where such conditions were found for simply-connected CW-complexes M, and Cencelj and Dranishnikov forthcoming paper [Cannad. Bull. Math.] where such conditions were found for nilpotent CW-complexes M with finitely generated homotopy groups.

MSC

55M10
55S36
54C20
54F45

Keywords

Cohomological dimension
Extension of maps
Nilpotent space

Cited by (0)

1

Supported in part by the Ministry of Science and Technology of Slovenia, Research Grant No. J1-0885-0101-98.