Gröbner Bases in the Mod 2 Cohomology of Oriented Grassmann Manifolds G^e<inf>2</inf>t<inf>,</inf><inf>3</inf>

Abstract

For n a power of two, we give a complete description of the cohomology algebra H∗(Gen,3; Z2) of the Grassmann manifold Gen,3 of oriented 3-planes in Rn. We do this by finding a reduced Gröbner basis for an ideal closely related to this cohomology algebra. Using this Gröbner basis we also present an additive basis for H∗(Gen,3; Z2).