Smash products for secondary homotopy groups
arXiv:math/0604031 · doi:10.1007/s10485-007-9071-x
Abstract
We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered. In particular we prove a formula for the crossed effect of the cup-one product operation on unstable homotopy groups of spheres which was claimed by Barratt-Jones-Mahowald.
We give a clearer description of the tensor product of symmetric sequences of quadratic pair modules