Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 10, Number 1 (2010), 33-61.
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 homotopy –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 –excisive functors of the form factor over the category of homotopy –nilpotent groups.
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
Permanent link to this document
Digital Object Identifier
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
Biedermann, Georg; Dwyer, William G. Homotopy nilpotent groups. Algebr. Geom. Topol. 10 (2010), no. 1, 33--61. doi:10.2140/agt.2010.10.33. https://projecteuclid.org/euclid.agt/1513882307