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In the paper On the mod p cohomology of BPU(p), the authors say that there is a conjecture of J. F. Adams as follows: Conjecture (J. F. Adams) Let $G$ be a compact connected Lie group, and let $p$ be ...

For purposes of my own, I'm interested in constructing connected spaces, without recourse to geometric realisation or the like, that have non-trivial homotopy groups in dimension 1 and 2 and are not ...