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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The $ H$-space squaring map on $ \Omega\sp 3S\sp {4n+1}$ factors through the double suspension


Author: William Richter
Journal: Proc. Amer. Math. Soc. 123 (1995), 3889-3900
MSC: Primary 55Q40; Secondary 55Q15, 55Q25
MathSciNet review: 1273520
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Abstract: We compute the first EHP spectral sequence differential followed by the double suspension. We show that $ 2{\pi _ \ast }({S^{4n + 1}}) \subset \operatorname{Im} ({E^2})$, which refines the exponent for $ {\pi _ \ast }({S^{2n + 1}})$ of James and Selick. The proof follows an odd primary program of Gray and Harper, and uses Barratt's theory of unsuspended Hopf invariants and Boardman and Steer's geometric Hopf invariants.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1273520-6
PII: S 0002-9939(1995)1273520-6
Keywords: James-Hopf invariants, Cartan formula, exponents, EHP fibrations
Article copyright: © Copyright 1995 American Mathematical Society