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 | References | Similar Articles | Additional Information
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.
- Mark Mahowald, The metastable homotopy of $S^{n}$, Memoirs of the American Mathematical Society, No. 72, American Mathematical Society, Providence, R.I., 1967. MR 0236923
- Robert E. Mosher, Some stable homotopy of complex projective space, Topology 7 (1968), 179–193. MR 227985, DOI https://doi.org/10.1016/0040-9383%2868%2990026-8
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Additional Information
Keywords:
Complex projective space,
quaternionic projective space,
Hurewicz homomorphism,
Adams spectral sequence
Article copyright:
© Copyright 1970
American Mathematical Society