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arXiv · 1612.02694

The $v_n$-periodic Goodwillie tower on Wedges and Cofibres

Lukas Brantner·Gijs Heuts
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Abstract

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 $\mathrm{cof}(f)$ of a map $f: X \rightarrow Y$. 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.

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Lukas Brantner, Gijs Heuts. 2016-12-08. The $v_n$-periodic Goodwillie tower on Wedges and Cofibres. https://arxiv.org/abs/1612.02694

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