Abstract
We shall study the relation between the unstable homotopy spectral sequence associated with the cell decomposition of the source space and the one associated with the Postnikov decomposition of the target space. It is proved that the Maunder's result holds for these two types of spectral sequences. This result will be exploited to study the differentials of these spectral sequences and we obtain a generalization of a theorem due to Atiyah-Hirzebruch and Dold. Making use of these spectral sequences with the convergence lemma, some results on the phantom maps and the homotopy groups of map*(Y, X) will be proved.
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Oda, N., Shitanda, Y. On the unstable homotopy spectral sequences. Manuscripta Math 56, 19–35 (1986). https://doi.org/10.1007/BF01171031
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DOI: https://doi.org/10.1007/BF01171031