Torsions of integral homology and cohomology of real Grassmannians

TL;DR

This paper computes the dimensions of 2-torsion parts in the integral homology and cohomology of real Grassmannians, extending understanding of their torsion structure.

Contribution

It provides explicit calculations of the $ ext{Z}_2$-dimensions of torsions in homology and cohomology, offering new insights into the torsion structure of real Grassmannians.

Findings

Torsions in integral homology of real Grassmannians are all of order 2.

Computed the $ ext{Z}_2$-dimensions of torsions in homology and cohomology.

Enhanced understanding of the torsion structure in real Grassmannians.

Abstract

According to a result of Ehresmann, the torsions of integral homology of real Grassmannian are all of order $2$. In this note, We compute the $\mathbb{Z}_2$-dimensions of torsions in the integral homology and cohomology of real Grassmannian.