ar X iv : 0 70 9 . 39 25 v 1 [ m at h . A T ] 2 5 Se p 20 07 HOMOTOPY NILPOTENT GROUPS
نویسنده
چکیده
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 π0 is the theory of ordinary n-nilpotent groups. Finally we prove, that the Goodwillie tower of a connected space is determined by a homotopy left Kan extension.
منابع مشابه
ar X iv : 0 70 9 . 39 25 v 2 [ m at h . A T ] 3 D ec 2 00 7 HOMOTOPY NILPOTENT GROUPS
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 π0 is the theory of ordinary n-nilpotent groups and that ...
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