On integral cohomology algebra of some oriented Grassmann manifolds

Abstract

The integral cohomology algebra of G˜6,3 has been determined in the recent work of Kalafat and Yalçınkaya. We completely determine the integral cohomology algebra of 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 G˜n,2 for n odd.