## Whitehead products as images of Pontrjagin products

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- by Martin Arkowitz PDF
- Trans. Amer. Math. Soc.
**158**(1971), 453-463 Request permission

## 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.## References

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**28**#1092.

## Additional Information

- © Copyright 1971 American Mathematical Society
- 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