Homotopy classification of module bundles via Grassmannians

Abstract

AbstractGiven a Waelbroeck ring R, we prove that the Grassmannian of a projective finitely generated R ‐module is a topological manifold modeled on a topological abelian group of R ‐linear maps. Fibre bundles of fibre type a module as above, over a compact base space B, admitting R ‐valued partitions of unity, are classified by the homotopy classes of continuous maps on B with values in the respective Grassmannian. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)