Cup-length of oriented Grassmann manifolds via Gröbner bases.

The aim of this paper is to prove a conjecture made by T. Fukaya in 2008. This conjecture concerns the exact value of the Z 2 -cup-length of the Grassmann manifold G ˜ n , 3 of oriented 3-planes in R n. Along the way, we calculate the heights of the Stiefel–Whitney classes of the canonical vector bundle over G ˜ n , 3. [ABSTRACT FROM AUTHOR]