We establish certain conditions which imply that a map $f:X\rightarrow Y$ 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.
Journal of Homotopy and Related Structures, Vol. 4(2009), No. 1, pp. 347-357