In the spirit of old questions, here's another one without an answer: can we get a "holomorphic model" for a K(Z,2)?
https://mathoverflow.net/q/237837/4177
#mathoverflow
Kuiper's theorem is well-known to give the triviality of the homotopy groups of ${\rm GL}(\mathcal{H})$ for $\mathcal{H}$ a (separable) infinite-dimensional complex Hilbert space. Work of Palais la...
theHigherGeometer