On the homotopy type of A(\Sigma(X))

TL;DR

This paper proves that for connected spaces, the functor mapping X to A(Σ(X)) decomposes homotopically into a product of its derivatives, clarifying its structure in algebraic topology.

Contribution

It provides a correct proof that the functor A(Σ(X)) splits up to homotopy into a product of its Goodwillie derivatives for connected spaces.

Findings

Confirmed the homotopy splitting of A(Σ(X)) into derivatives.

Corrected previous proofs regarding the functor's structure.

Enhanced understanding of the functor's behavior in algebraic topology.

Abstract

We give a correct proof that for all connected spaces X, the functor X |-> A(\Sigma(X)) splits up to homotopy as a product of its Goodwillie derivatives.