The vn-periodic goodwillie tower on wedges and cofibres
Publication date
2020-01-01
Authors
Brantner, Lukas
Heuts, Gijs
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Document Type
Article
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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.
Keywords
Goodwillie calculus, Hilton-Milnor theorem, vn-periodicity, Taverne, Mathematics (miscellaneous)
Citation
Brantner, L & Heuts, G 2020, 'The v n -periodic goodwillie tower on wedges and cofibres', Homology, Homotopy and Applications, vol. 22, no. 1, pp. 167-184. https://doi.org/10.4310/HHA.2020.v22.n1.a10