On the stable homotopy of quaternionic and complex projective spaces.
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- by David M. Segal
- Proc. Amer. Math. Soc. 25 (1970), 838-841
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259914-9
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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
- 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 10.1016/0040-9383(68)90026-8
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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