Smash products for secondary homotopy groups

Details Smash products for secondary homotopy groups Smash products for secondary homotopy groups

2006-04-03

arxiv.org/abs/math/0604031v2

Appl. Categ. Structures, 16 (2008) no. 5, 551-616

Mathematics

Algebraic Topology

We give a clearer description of the tensor product of symmetric sequences of quadratic pair modules

Scientific paper

10.1007/s10485-007-9071-x

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.

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