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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the stable homotopy of quaternionic and complex projective spaces.


Author: David M. Segal
Journal: Proc. Amer. Math. Soc. 25 (1970), 838-841
MSC: Primary 55.45
DOI: https://doi.org/10.1090/S0002-9939-1970-0259914-9
MathSciNet review: 0259914
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Abstract: Let the image in $ {H_{4k}}({\operatorname{QP} ^\infty }:Z) = Z$ of stable homotopy under the Hurewicz homomorphism be $ h(k) \cdot Z$. Using the Adams spectral sequence for the $ 2$-primary stable homotopy of quaternionic and complex projective spaces it is shown that $ h(k)$ is $ (2k)!$ if $ k$ is even and is $ (2k)!/2$ if $ k$ is odd.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0259914-9
Keywords: Complex projective space, quaternionic projective space, Hurewicz homomorphism, Adams spectral sequence
Article copyright: © Copyright 1970 American Mathematical Society