On integral cohomology algebra of some oriented Grassmann manifolds

TL;DR

This paper computes the integral cohomology algebras of certain oriented Grassmann manifolds, extending previous results to specific cases and illustrating the method with additional examples.

Contribution

It provides explicit descriptions of the integral cohomology algebras for  and 0, and demonstrates the use of the Leray-Serre spectral sequence for these computations.

Findings

Integral cohomology algebra of  and 0 Grassmann manifolds determined.

Method applied to , 0, and  cases, illustrating its effectiveness.

Extends previous work on ,3 to additional dimensions.

Abstract

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.