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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Pairings and products in the homotopy spectral sequence

Authors: A. K. Bousfield and D. M. Kan
Journal: Trans. Amer. Math. Soc. 177 (1973), 319-343
MSC: Primary 55H15
MathSciNet review: 0372860
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Abstract: Smash and composition pairings, as well as Whitehead products are constructed in the unstable Adams spectral sequence; and these pairings and products are described homologically on the $ {E_2}$. level. In the special case of the Massey-Peterson spectral sequence, the composition action is given homologically by the Yoneda product, while the Whitehead product vanishes. It is also shown that the unstable Adams spectral sequence over the rationals, with its Whitehead products, is given by the primitive elements in the rational cobar spectral sequence.

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Keywords: Unstable Adams spectral sequence, simplicial set, cosimplicial resolution, composition pairing, Whitehead product
Article copyright: © Copyright 1973 American Mathematical Society