A note on the second James-Hopf invariant

Abstract

This paper characterizes the stabilized second James-Hopf invariant by means of three axioms. Specifically, we show that it is the unique natural transformation satisfying the Cartan formula, vanishing on suspensions. The proof combines the natural stable splitting of the James construction with Goodwillie calculus.

I am grateful to Nick Kuhn for explaining why the EHP property is not necessary