Gröbner bases of oriented Grassmann manifolds

Abstract

For n = 2 m+1 -4, m 2, we determine the cup-length of H * ( G n,3 ; Z/2) by finding a Gröbner basis associated with a certain subring, where G n,3 is the oriented Grassmann manifold SO(n + 3)/SO(n) × SO(3).As an application, we provide not only a lower but also an upper bound for the LS-category of G n,3 .We also study the immersion problem of G n,3 .