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Extension of Maps to Nilpotent Spaces |
Published:2001-09-01
Printed: Sep 2001
Printed: Sep 2001
- M. Cencelj
- A. N. Dranishnikov
Abstract
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 $\CW$-complex $M$ with finitely
generated homotopy groups over all of $X$.
| Keywords: | cohomological dimension, extension of maps, nilpotent group, nilpotent space |
| MSC Classifications: |
55M10 - Dimension theory [See also 54F45] 55S36 - Extension and compression of mappings 54C20 - Extension of maps 54F45 - Dimension theory [See also 55M10] |