Goodwillie calculus and Whitehead products
Jerome Scherer, Boris Chorny
TL;DR
This paper explores the relationship between Goodwillie calculus and Whitehead products, proving vanishing results for iterated Whitehead products in n-excisive functors and comparing notions of homotopy nilpotency.
Contribution
It establishes a connection between Whitehead product vanishing and n-excisive functors, and compares different homotopy nilpotency notions within this context.
Findings
Iterated Whitehead products of length (n+1) vanish in n-excisive functors.
Different notions of homotopy nilpotency are compared, highlighting their relation to Goodwillie calculus.
Analysis of Whitehead products provides insights into homotopy-theoretic properties of functors.
Abstract
We prove that iterated Whitehead products of length (n+1) vanish in any value of an n-excisive functor in the sense of Goodwillie. We compare then different notions of homotopy nilpotency, from the Berstein-Ganea definition to the Biedermann-Dwyer one. The latter is strongly related to Goodwillie calculus and we analyze the vanishing of iterated Whitehead products in such objects.
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