The Higher Structure of Unstable Homotopy Groups

Authors

Samik Basu, Indian Statistical Institute, Kolkata
David Blanc, University of Haifa
Debasis Sen, Indian Institute of Technology Kanpur

Article Type

Research Article

Publication Title

International Mathematics Research Notices

Abstract

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.

First Page

5815

Last Page

5849

DOI

10.1093/imrn/rnad250

Publication Date

4-1-2024

Comments

Open Access; Green Open Access

Recommended Citation

Basu, Samik; Blanc, David; and Sen, Debasis, "The Higher Structure of Unstable Homotopy Groups" (2024). Journal Articles. 5142.
https://digitalcommons.isical.ac.in/journal-articles/5142