homotopy – Konrad Voelkel's Blog – Mathemagically

Is it possible to prove the Quillen-Suslin theorem analogous to the classical theorem on vector bundles over contractible spaces via representing the vectorbundle-up-to-iso-functor in the homotopy category by infinite Grassmannians?

Definition of essential manifolds, lens spaces as example of non-aspherical essential manifolds.

Aspherical manifolds, Eilenberg-MacLane spaces, classifying spaces of groups via the nerve construction.

Diplomarbeit von Konrad Völkel (auf deutsch).