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 $n$ –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 $Ω F$ factor over the category of homotopy $n$ –nilpotent groups.

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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

Volume 10, issue 1 (2010)

Georg Biedermann and William G Dwyer

Abstract