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arXiv · 2003.08842

The higher structure of unstable homotopy groups

Samik Basu·David Blanc·Debasis Sen
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Abstract

We construct certain unstable higher-order homotopy operations indexed by the simplex categories of $\Delta^{n}$ for ${n\geq 2}$ and prove that all elements in the homotopy groups of a wedge of spheres are generated under such operations by Whitehead products and the group structure. This provides a stronger unstable analogue of Cohen's theorem on the decomposition of stable homotopy.

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Samik Basu, David Blanc, Debasis Sen. 2020-03-19. The higher structure of unstable homotopy groups. https://doi.org/10.1093/imrn/rnad250

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