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

TL;DR

This paper uses Groebner bases to compute the cup-length of oriented Grassmann manifolds, providing bounds for their LS-category and insights into their immersion properties.

Contribution

It introduces a method to determine cup-length via Groebner bases and applies this to estimate LS-category and study immersions of these manifolds.

Findings

Cup-length of certain oriented Grassmann manifolds determined

Bounds for LS-category established

Insights into immersion problems provided

Abstract

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.