Classifying spaces for commutativity of low-dimensional Lie groups

Omar Antolín-Camarena, Simon Gritschacher, Bernardo Villarreal

For each of the groups $G=O(2),SU(2),U(2)$, we compute the integral and ${\mathbb{F}}_2$-cohomology rings of $B_{\text{com}}G$ (the classifying space for commutativity of $G$), th…