Geodesic
The $v_n$-periodic Goodwillie tower on wedges and cofibres
Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 167-184.

Voir la notice de l'article provenant de la source International Press of Boston

We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge $X \vee Y$ of spaces (using the Hilton–Milnor theorem) and on the cofibre $\operatorname{cof}(f)$ of a map $f : X \to Y $ We deduce some consequences for $v_n$-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.
DOI : 10.4310/HHA.2020.v22.n1.a10
Classification : 55Q20, 55Q51
Keywords: Goodwillie calculus, $v_n$-periodicity, Hilton–Milnor theorem 
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     author = {Lukas Brantner and Gijs Heuts},
     title = {The $v_n$-periodic {Goodwillie} tower on wedges and cofibres},
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Lukas Brantner; Gijs Heuts. The $v_n$-periodic Goodwillie tower on wedges and cofibres. Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 167-184. doi : 10.4310/HHA.2020.v22.n1.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n1.a10/

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