Homotopy nilpotent groups

Details Homotopy nilpotent groups Homotopy nilpotent groups

2007-09-25

arxiv.org/abs/0709.3925v4

Mathematics

Algebraic Topology

16 pages, uses xy-pic, improved exposition, submitted

Scientific paper

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 $\pi_0$ 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 $\Omega F$ have values in homotopy n-nilpotent groups.

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