Hi all, I am new to topology & geometry. I skimmed through the subject in various books so I might be asking simple questions. My question is how can we say Chern's class belong to Integer rather than Real cohomology class? I assume one defines it through the characteristic polynomial of the curvature form. (as in http://en.wikipedia.org/wiki/Chern_class) It does not look obvious to me this make chern's class belong to integral cohomology. I think this is important so that Chern's numbers are integers.