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Jan 2, 2016 at 14:51 comment added André Henriques Yes indeed. And so will any non-trivial $G$-bundle on a $K(\pi,1)$ (a surface; a 3-manifold, etc...) when $G$ is a connected Lie group.
Jan 2, 2016 at 8:50 comment added Tom Church Any other circle bundle over the 2-torus will work as well, won't it?
Dec 30, 2015 at 0:53 history answered André Henriques CC BY-SA 3.0