Classifying spaces for commutativity of low-dimensional Lie groups

Abstract

AbstractFor each of the groups G = O(2), SU(2), U(2), we compute the integral and $\mathbb{F}_2$-cohomology rings of BcomG (the classifying space for commutativity of G), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy type of EcomG (the homotopy fiber of the inclusion BcomG → BG), and some low-dimensional homotopy groups of BcomG.