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Extension of Maps to Nilpotent Spaces

Published online by Cambridge University Press:  20 November 2018

M. Cencelj  and
A. N. Dranishnikov
M. Cencelj
Affiliation:
IMFM University of Ljubljana P. O. B. 2964 SI-1001 Ljubljana Slovenia, e-mail: matija.cencelj@uni-lj.si
A. N. Dranishnikov
Affiliation:
Pennsylvania State University Mathematics Department 218 McAllister Building University Park, Pennsylvania 16802 U.S.A., e-mail: dranish@math.psu.edu
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Abstract

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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 $X$ .

Keywords

55M1055S3654C2054F45cohomological dimensionextension of mapsnilpotent groupnilpotent space

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 3 , 01 September 2001 , pp. 266 - 269
Copyright
Copyright © Canadian Mathematical Society 2001

References

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