On the homotopy classification of maps

We establish certain conditions which imply that a map \(f:X\to Y\) of topological spaces is null homotopic when the induced integral cohomology homomorphism is trivial; one of them is: \(H^*(X)\) and \(\pi_*(Y)\) have no torsion and \(H^*(Y)\) is polynomial.

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Bibliographic Details
Published in:arXiv.org 2009-06
Main Author: Samson Saneblidze
Format: Article
Language:English
Subjects:
Homology
Homomorphisms
Polynomials
Online Access:Get full text
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Description
Summary:We establish certain conditions which imply that a map \(f:X\to Y\) of topological spaces is null homotopic when the induced integral cohomology homomorphism is trivial; one of them is: \(H^*(X)\) and \(\pi_*(Y)\) have no torsion and \(H^*(Y)\) is polynomial.
ISSN:2331-8422