Relative Gottlieb Groups of Embeddings between Complex Grassmannians

Abstract

Let $\text{Gr}\left(k,n\right)$ be the complex Grassmann manifold of $k$ -linear subspaces in ${ℂ}^n$ . We compute rational relative Gottlieb groups of the embedding $i:\text{Gr}\left(k,n\right)⟶\text{Gr}\left(k,n+r\right)$ and show that the $G$ -sequence is exact if $r\ge k\left(n-k\right)$ .