Geodesic
Extension of Maps to Nilpotent Spaces
Canadian mathematical bulletin, Tome 44 (2001) no. 3, pp. 266-269

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DOI

We show that every compactum has cohomological dimension 1 with respect to a finitely generated nilpotent group $G$ whenever it has cohomological dimension 1 with respect to the abelianization of $G$ . This is applied to the extension theory to obtain a cohomological dimension theory condition for a finite-dimensional compactum $X$ for extendability of every map from a closed subset of $X$ into a nilpotent $\text{CW}$ -complex $M$ with finitely generated homotopy groups over all of $X$ .
DOI : 10.4153/CMB-2001-026-1
Mots-clés : 55M10, 55S36, 54C20, 54F45, cohomological dimension, extension of maps, nilpotent group, nilpotent space 
Cencelj, M.; Dranishnikov, A. N. Extension of Maps to Nilpotent Spaces. Canadian mathematical bulletin, Tome 44 (2001) no. 3, pp. 266-269. doi: 10.4153/CMB-2001-026-1
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     title = {Extension of {Maps} to {Nilpotent} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {266--269},
     year = {2001},
     volume = {44},
     number = {3},
     doi = {10.4153/CMB-2001-026-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-026-1/}
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