The Higher Structure of Unstable Homotopy Groups

Samik Basu, David Blanc, Debasis Sen

Research output: Contribution to journalArticlepeer-review


We construct certain unstable higher order homotopy operations indexed by the simplex categories of deltan for n ≥ 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.

Original languageAmerican English
Pages (from-to)5815-5849
Number of pages35
JournalInternational Mathematics Research Notices
Issue number7
StatePublished - 1 Apr 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics


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