The purpose of this article is to show a simple method of finding $\mathbb Z_2$-Betti numbers of oriented Grassmannians. The actual calculation is performed by computing $\mathbb Z_2$-ranks of matrices defined in a combinatorial way. For the reduction of problem from topology to matrix rank, we will analyse Morse homology of certain functions on the oriented Grassmannians.
The author would like to thank Professor Toshiaki Maeno for valuable comments.
"The $\mathbb Z_2$-Betti numbers of oriented Grassmannians." Osaka J. Math. 59 (4) 843 - 851, October 2022.