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2 results

Some results on extension of maps and applications
Part of
Carlos Biasi, Alice K. M. Libardi, Thiago de Melo, Edivaldo L. dos Santos
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 6 / December 2019

Published online by Cambridge University Press:

16 January 2019, pp. 1465-1472

Print publication:

December 2019
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This paper concerns extension of maps using obstruction theory under a non-classical viewpoint. It is given a classification of homotopy classes of maps and as an application it is presented a simple proof of a theorem by Adachi about equivalence of vector bundles. Also it is proved that, under certain conditions, two embeddings are homotopic up to surgery if and only if the respective normal bundles are SO-equivalent.

Extension of Maps to Nilpotent Spaces
M. Cencelj, A. N. Dranishnikov
Journal:

Canadian Mathematical Bulletin / Volume 44 / Issue 3 / 01 September 2001

Published online by Cambridge University Press:

20 November 2018, pp. 266-269

Print publication:

01 September 2001
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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 $X$.