Geometry & Topology
- Geom. Topol.
- Volume 11, Number 1 (2007), 315-427.
Discrete models for the $p$–local homotopy theory of compact Lie groups and $p$–compact groups
We define and study a certain class of spaces which includes –completed classifying spaces of compact Lie groups, classifying spaces of –compact groups, and –completed classifying spaces of certain locally finite discrete groups. These spaces are determined by fusion and linking systems over “discrete –toral groups”—extensions of by finite –groups—in the same way that classifying spaces of –local finite groups as defined in our paper [The homotopy theory of fusion systems, J. Amer. Math. Soc. 16 (2003) 779–856] are determined by fusion and linking systems over finite –groups. We call these structures “–local compact groups”.
Geom. Topol., Volume 11, Number 1 (2007), 315-427.
Received: 19 July 2006
Accepted: 20 November 2006
First available in Project Euclid: 20 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: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20] 57T10: Homology and cohomology of Lie groups
Broto, Carles; Levi, Ran; Oliver, Bob. Discrete models for the $p$–local homotopy theory of compact Lie groups and $p$–compact groups. Geom. Topol. 11 (2007), no. 1, 315--427. doi:10.2140/gt.2007.11.315. https://projecteuclid.org/euclid.gt/1513799836