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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.


References [Enhancements On Off] (What's this?)

  • [1] M. Mahowald, The metastable homotopy of $ {S^n}$, Mem. Amer. Math. Soc., No. 72 (1967). MR 0236923 (38:5216)
  • [2] R. E. Mosher, Some stable homotopy of complex projective spaces, Topology 7 (1968), 179-193. MR 37 #3569. MR 0227985 (37:3569)

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Additional Information

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

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