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The symmetric action on secondary homotopy groups

Hans-Joachim Baues·Fernando Muro
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Abstract

We show that the symmetric track group, which is an extension of the symmetric group associated to the second Stiefel- Withney class, acts as a crossed module on the secondary homotopy group of a pointed space. An application is given to cup-one products in unstable homotopy groups of spheres, generalizing a formula of Barratt-Jones-Mahowald.

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Hans-Joachim Baues, Fernando Muro. 2006-10-17. The symmetric action on secondary homotopy groups. https://arxiv.org/abs/math/0604030

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