Cohomology rings of oriented Grassmann manifolds $\tilde{G}_{2^t, 4}$

Abstract

We give a description of the mod 2 cohomology algebra of the oriented Grassmann manifold $\tilde{G}_{2^t, 4}$ as the quotient of a polynomial algebra by a certain ideal. In the process we find a Gröbner basis for that ideal, which we then use to exhibit an additive basis for $H⁎(\tilda{G}_{2^t, 4} ; Z_2)$.