Minimal models of Grassmann manifolds and applications

Abstract

We construct the minimal models for the oriented Grassmann manifold G_n,k of all oriented k dimensional vector subspaces of Rⁿ and verify that they are formal. As an application we obtain a classification of real flag manifolds according to nilpotence, which was first established by H. Glover and W.Homer. We also establish a result of K. Varadarajan that the classifying space BO(k) is nilpotent if and only if k is odd.