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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Keywords: James-Hopf invariants, Cartan formula, exponents, EHP fibrations
Article copyright: © Copyright 1995 American Mathematical Society