Abstract
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.
Citation
Alejandro Adem. José Gómez. "A classifying space for commutativity in Lie groups." Algebr. Geom. Topol. 15 (1) 493 - 535, 2015. https://doi.org/10.2140/agt.2015.15.493
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