Minimal models of Grassmann manifolds and applications

Sankaran, Parameswaran ; Mukherjee, G. (2000) Minimal models of Grassmann manifolds and applications Mathematica Slovaca, 50 (5). pp. 567-579. ISSN 0139-9918

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Abstract

We construct the minimal models for the oriented Grassmann manifold Gn,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.

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