Application of Groebner bases to the cup-length of oriented Grassmann manifolds

الأصل · EN

We determine the cup-length of some oriented Grassmann manifolds by finding a Groebner basis associated with a certain subring of the cohomology of them. As its applications, we provide not only a lower but also an upper bound for the LS-category of some oriented Grassmann manifolds. We also study the immersion problem of them.