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arXiv · 0709.3925

Homotopy nilpotent groups

Georg Biedermann·William G. Dwyer
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Abstract

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove that the set-valued algebraic theory obtained by applying $π_0$ is the theory of ordinary n-nilpotent groups and that the Goodwillie tower of a connected space is determined by a certain homotopy left Kan extension. We prove that n-excisive functors of the form $ΩF$ have values in homotopy n-nilpotent groups.

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Georg Biedermann, William G. Dwyer. 2008-04-11. Homotopy nilpotent groups. https://doi.org/10.2140/agt.2010.10.33

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