The vn-periodic goodwillie tower on wedges and cofibres

Abstract

We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge X ∨ Y of spaces (using the Hilton-Milnor theorem) and on the cofibre cof(f) of a map f: X → Y. We deduce some consequences for vn-periodic homotopy groups: whereas the Goodwillie tower is finite and converges in periodic homotopy when evaluated on spheres (Arone-Mahowald), we show that neither of these statements remains true for wedges and Moore spaces.