Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠ 2 t,3

Abstract

Abstract For n a power of two, we give a complete description of the cohomology algebra H *(G͠ n,3; ℤ2) of the Grassmann manifold G͠ n,3 of oriented 3-planes in ℝ n . 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 *(G͠ n,3; ℤ2).