Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 5 (2014), 2915-2982.
An algebraic model for finite loop spaces
A –local compact group consists of a discrete –toral group , together with a fusion system and a linking system over which define a classifying space having very nice homotopy properties. We prove here that if some finite regular cover of a space is the classifying space of a –local compact group, then so is . Together with earlier results by Dwyer and Wilkerson and by the authors, this implies as a special case that a finite loop space determines a –local compact group at each prime .
Algebr. Geom. Topol., Volume 14, Number 5 (2014), 2915-2982.
Received: 13 August 2013
Revised: 27 February 2014
Accepted: 3 March 2014
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure 20E22: Extensions, wreath products, and other compositions [See also 20J05]
Broto, Carles; Levi, Ran; Oliver, Bob. An algebraic model for finite loop spaces. Algebr. Geom. Topol. 14 (2014), no. 5, 2915--2982. doi:10.2140/agt.2014.14.2915. https://projecteuclid.org/euclid.agt/1513716006