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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Self-maps of projective spaces


Author: C. A. McGibbon
Journal: Trans. Amer. Math. Soc. 271 (1982), 325-346
MSC: Primary 55P40; Secondary 55S25
DOI: https://doi.org/10.1090/S0002-9947-1982-0648096-X
MathSciNet review: 648096
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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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DOI: https://doi.org/10.1090/S0002-9947-1982-0648096-X
Keywords: Projective $ n$-space, suspension, Adams $ e$-invariant, Hopf bundle, Vandermonde determinant, Maclaurin's series, genus of a nilpotent homotopy type, Lefschetz number, order of the identity
Article copyright: © Copyright 1982 American Mathematical Society

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