English

The symmetric action on secondary homotopy groups

Algebraic Topology 2009-08-04 v2 Category Theory

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.

Keywords

Cite

@article{arxiv.math/0604030,
  title  = {The symmetric action on secondary homotopy groups},
  author = {Hans-Joachim Baues and Fernando Muro},
  journal= {arXiv preprint arXiv:math/0604030},
  year   = {2009}
}

Comments

We correct a misprint in the presentation of the symmetric track groups

R2 v1 2026-07-22T17:33:41.836Z