Volume 10, issue 1 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Homotopy nilpotent groups

Georg Biedermann and William G Dwyer

Algebraic & Geometric Topology 10 (2010) 33–61
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 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.

Keywords
Goodwillie tower, excisive functors, loop group, lower central series, loop space, infinite loop spaces, homotopy nilpotent groups, algebraic theories
Mathematical Subject Classification 2000
Primary: 55P47, 55U35
Secondary: 18C10, 55P35
References
Publication
Received: 16 September 2009
Revised: 2 October 2009
Accepted: 7 October 2009
Published: 2 January 2010
Authors
Georg Biedermann
Departamento de Matemáticas
Universidad de los Andes
Cr 1a No 18A 10
Bogotá
Colombia
http://matematicas.uniandes.edu.co/~gbiederm
William G Dwyer
Department of Mathematics
255 Hurley
University of Notre Dame
Notre Dame IN 46556
USA
http://www.math.nd.edu/~dwyer