The integral cohomology algebra of $\widetilde G_{ 6,3}$ has been determined in the recent work of Kalafat and Yal\c{ c}inkaya. We completely determine the integral cohomology algebra of $\widetilde G_{ n,3}$ for $n=8$ and $n=10$. The main method used to describe these algebras is the Leray-Serre spectral sequence. We also illustrate this method by determining the integral cohomology algebra of $\widetilde G_{ n,2}$ for $n$ odd.
Categories: math.AT