Torsions of integral homology and cohomology of 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.

arXiv comment6 pages with codes