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Mar 4, 2020 at 19:46 comment added Sebastian Goette @RobertFurber That's right. And because $BO(1)$ and $BU(1)$ are Eilenberg-Mac Lane spaces, you can immediately classify real and complex line bundles by a single cohomology class. But not quaternionic line bundles.
Mar 3, 2020 at 15:55 comment added Robert Furber Although it's not an Eilenberg-MacLane space, $\mathbb{HP}^\infty$ is a classifying space (specifically $B(SU(2))$), just as $\mathbb{CP}^\infty = B(U(1))$ and $\mathbb{RP}^\infty = B(\mathbb{Z}/(2))$.
S Jan 29, 2016 at 13:59 history answered Sebastian Goette CC BY-SA 3.0
S Jan 29, 2016 at 13:59 history made wiki Post Made Community Wiki by Sebastian Goette