Gröbner bases for some flag manifolds and applications

Abstract

The mod 2 cohomology of the real flag manifolds is known to be isomorphic to a polynomial algebra modulo a certain ideal. In this paper reduced Gröbner bases for these ideals are obtained in the case of manifolds F(1, ⋯, 1, 2, ⋯, 2, n). As an application of this result, the appropriate Stiefel-Whitney classes are calculated and some new non-embedding and non-immersion theorems for some manifolds of this type are obtained.