International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 21, Pages 3487-3495
doi:10.1155/IJMMS.2005.3487
Flat circle bundles, pullbacks, and the circle made discrete
John Oprea1
and Daniel Tanré2
1Department of Mathematics, Cleveland State University, Cleveland 44115-2214, OH, USA
2Département de Mathématiques, Université de Lille 1, Villeneuve d'Ascq Cedex 59655, France
Abstract
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.