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Transactions of the American Mathematical Society

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

 
 

 

Whitehead products as images of Pontrjagin products


Author: Martin Arkowitz
Journal: Trans. Amer. Math. Soc. 158 (1971), 453-463
MSC: Primary 55.40
DOI: https://doi.org/10.1090/S0002-9947-1971-0278300-4
MathSciNet review: 0278300
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Abstract: A method is given for computing higher order Whitehead products in the homotopy groups of a space $X$. If $X$ can be embedded in an $H$-space $E$ such that the pair $(E,X)$ has sufficiently high connectivity, then we prove that a higher order Whitehead product element in the homotopy of $X$ is the homomorphic image of a Pontrjagin product in the homology of $E$. The two main applications determine a higher order Whitehead product element in (1) ${\pi _ \ast }(B{U_t})$, the homotopy groups of the classifying space of the unitary group ${U_t}$, (2) the homotopy groups of a space with two nonvanishing homotopy groups.


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Keywords: Whitehead product, higher order Whitehead product, Pontrjagin product, Postnikov systems, Samelson product, classifying space of the unitary group, Eilenberg-MacLane complex
Article copyright: © Copyright 1971 American Mathematical Society