Self-maps of projective spaces

McGibbon, C. A.

doi:10.1090/S0002-9947-1982-0648096-X

Self-maps of projective spaces
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by C. A. McGibbon

Trans. Amer. Math. Soc. 271 (1982), 325-346

DOI: https://doi.org/10.1090/S0002-9947-1982-0648096-X

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Abstract:

The classical projective $n$-spaces (real, complex, and quaternionic) are studied in terms of their self maps, from a homotopy point of view. Self maps of iterated suspensions of these spaces are also considered. The goal in both cases is to classify, up to homology, all such maps. This goal is achieved in the stable case. Some partial results are obtained in the unstable case. The results from both cases are used to compute the genus groups and the stable genus groups of the classical projective spaces. Applications to other spaces are also given.

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localization, periodicity, and Galois symmetry

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