The symmetric action on secondary homotopy groups

Details The symmetric action on secondary homotopy groups The symmetric action on secondary homotopy groups

2006-04-03

arxiv.org/abs/math/0604030v2

Bull. Belg. Math. Soc. Simon Stevin 15 (2008) no. 4, 733-768

Mathematics

Algebraic Topology

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

Scientific paper

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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