On the mod 2 cohomology algebra of oriented Grassmannians

Abstract

For n∈{2t-3,2t-2,2t-1}(t≥3) we study the cohomology algebra H∗(G~n,3;Z2) of the Grassmann manifold G~n,3 of oriented 3-dimensional subspaces of Rn. A complete description of H∗(G~n,3;Z2) is given in the cases n=2t-3 and n=2t-2, while in the case n=2t-1 we obtain a description complete up to a coefficient from Z2.