Algebraic & Geometric Topology

Homotopy nilpotent groups

Georg Biedermann and William G Dwyer

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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 homotopy n–nilpotent groups as homotopy algebras over certain simplicial algebraic theories. This notion interpolates between infinite loop spaces and loop spaces, but backwards. We study the relation to ordinary nilpotent groups. We prove that n–excisive functors of the form ΩF factor over the category of homotopy n–nilpotent groups.

Article information

Algebr. Geom. Topol., Volume 10, Number 1 (2010), 33-61.

Received: 16 September 2009
Revised: 2 October 2009
Accepted: 7 October 2009
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P47: Infinite loop spaces 55U35: Abstract and axiomatic homotopy theory
Secondary: 18C10: Theories (e.g. algebraic theories), structure, and semantics [See also 03G30] 55P35: Loop spaces

Goodwillie tower excisive functors loop group lower central series loop space infinite loop spaces homotopy nilpotent groups algebraic theories


Biedermann, Georg; Dwyer, William G. Homotopy nilpotent groups. Algebr. Geom. Topol. 10 (2010), no. 1, 33--61. doi:10.2140/agt.2010.10.33.

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