Homotopy nilpotent groups
| Autor: | Georg Biedermann, William G. Dwyer |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Pure mathematics
Homotopical algebra excisive functors 18C10 Central series Mathematics::Algebraic Topology 55U35 55P35 55P47 algebraic theories Mathematics::K-Theory and Homology Loop group Mathematics::Category Theory infinite loop spaces FOS: Mathematics Goodwillie tower Algebraic Topology (math.AT) Mathematics - Algebraic Topology lower central series 55P35 55U35 Mathematics Functor Homotopy Tower (mathematics) loop space homotopy nilpotent groups Loop space loop group Simplicial set 55P47 Geometry and Topology |
| Zdroj: | Algebraic & Geometric Topology Algebr. Geom. Topol. 10, no. 1 (2010), 33-61 |
| DOI: | 10.48550/arxiv.0709.3925 |
| Popis: | 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 $\pi_0$ is the theory of ordinary n-nilpotent groups and that the Goodwillie tower of a connected space is determined by a certain homotopy left Kan extension. We prove that n-excisive functors of the form $\Omega F$ have values in homotopy n-nilpotent groups. Comment: 16 pages, uses xy-pic, improved exposition, submitted |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|