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Self Maps of Projective Spaces

C. A. McGibbon
Transactions of the American Mathematical Society
Vol. 271, No. 1 (May, 1982), pp. 325-346
DOI: 10.2307/1998769
Stable URL: http://www.jstor.org/stable/1998769
Page Count: 22
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Self Maps of Projective Spaces
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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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