Flat circle bundles, pullbacks, and the circle made discrete

John Oprea, Daniel Tanré
2005 International Journal of Mathematics and Mathematical Sciences  
We use basic homotopical methods applied to Lie groups made discrete to prove that the real Euler class of a circle bundle vanishes if and only if the bundle is flat.
doi:10.1155/ijmms.2005.3487 fatcat:2k223v7oyngklpap4bt4rhabdi