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Extension of Maps to Nilpotent Spaces
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AbstractWe 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 CW-complex M with finitely generated homotopy groups over all of X.
Title: Extension of Maps to Nilpotent Spaces
Description:
AbstractWe 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 CW-complex M with finitely generated homotopy groups over all of X.
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