The Yang indices of Grassmannians

Abstract

An elementary combinatorial technique for computing lower bounds for the Yang indices of real Stiefel manifolds and oriented real Grassmannians is described. As a demonstration, it shown that the Yang index of $St(n,k)$, and consequently $G(n,k)$, is at least $n - k$. For odd $n$, the bound for $G(n,2)$ can be improved to $n-1$. These are combined with basic properties of the Yang index and Conner-Floyd index and coindex to compute the possible Yang indices of $St(n,k)$ and $G(n,k)$ for small $n$.