Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 1 (2015), 493-535.
A classifying space for commutativity in Lie groups
In this article we consider a space assembled from commuting elements in a Lie group first defined by Adem, Cohen and Torres-Giese. We describe homotopy-theoretic properties of these spaces using homotopy colimits, and their role as a classifying space for transitionally commutative bundles. We prove that is a loop space and define a notion of commutative K–theory for bundles over a finite complex , which is isomorphic to . We compute the rational cohomology of for equal to any of the classical groups , and , and exhibit the rational cohomologies of , and as explicit polynomial rings.
Algebr. Geom. Topol., Volume 15, Number 1 (2015), 493-535.
Received: 9 June 2014
Revised: 10 July 2014
Accepted: 11 July 2014
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E99: None of the above, but in this section
Secondary: 55R35: Classifying spaces of groups and $H$-spaces
Adem, Alejandro; Gómez, José. A classifying space for commutativity in Lie groups. Algebr. Geom. Topol. 15 (2015), no. 1, 493--535. doi:10.2140/agt.2015.15.493. https://projecteuclid.org/euclid.agt/1510840921