Subject: formal bundles From: Claude Schochet Date: Thu, 22 Jun 2006 07:24:47 -0400 (EDT) for toplist Suppose that G is a compact Lie group (G = PU_k in my situation) , X is a finite complex (smooth manifold if you like) and f; X \to BG . Now suppose that X is formal in the sense of rational homotopy theory. (The space BG is automatically formal.) I am looking at fibre bundles classified by f. (In the case at hand the universal fibre bundle has the form U_k \to W \to BPU_k.) Question--- when is the map f formal? I am looking for geometrically meaningful statements about the pullback bundle or its associated principal G-bundle that imply that f is formal. For instance, is the formality of f equivalent to some conditions on the rational Chern classes of the bundle? I do not want to assume further conditions on X other than its being connected and nilpotent. Thanks! Claude ---------------------------------- Claude Schochet Math Dept, Wayne State University Detroit, MI 48202 claude@math.wayne.edu