Homotopy classification the J. H. C. Withehead way (Q1108609)

The author's purpose is to point out J. H. C. Whitehead's results about homotopy classification [\textit{J. H. C. Whithehead}, Bull. Am. Math. Soc. 55, 453-496 (1949; Zbl 0040.388)] as ``a standard piece of elementary topology''. The author recalls the relevant definitions and theorems from Whitehead's paper and uses the notions of equivariant cohomology and twisted degree to obtain three classification results as corollaries. As an application of these corollaries the author recovers some results of \textit{P. Olum} [Mappings of manifolds and the notion of degree, Ann. Math., II. Ser. 58, 458-480 (1953; Zbl 0052.199)] and a result of \textit{S. Jajodia} [Homotopy classification of lens spaces for one-relator groups with torsion, Pac. J. Math. 89, 301-311 (1980; Zbl 0458.55005)].