Extension of Maps to Nilpotent Spaces

Canadian mathematical bulletin

关键词: cohomological dimension;    extension of maps;    nilpotent group;    nilpotent space;   

DOI  :  10.4153/CMB-2001-026-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We show that every compactum has cohomological dimension $1$ with respectto a finitely generated nilpotent group $G$ whenever it has cohomologicaldimension $1$ with respect to the abelianization of $G$. This is appliedto the extension theory to obtain a cohomological dimension theory conditionfor a finite-dimensional compactum $X$ for extendability of every map froma closed subset of $X$ into a nilpotent $CW$-complex $M$ with finitelygenerated homotopy groups over all of $X$.

【 授权许可】

Unknown