We consider the complex Grassmannian Gr k , n of k -dimensional subspaces of ℂ n . There is a natural inclusion i n , r : Gr k , n ↪ Gr k , n + r . Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion i n , r in the space of mappings from Gr k , n to Gr k , n + r for r ≥ 1 and in particular to show that the cohomology of map Gr n , k , Gr n , k + r ; i n , r contains a truncated algebra ℚ x / x r + n + k 2 − n k , where x = 2 , for k ≥ 2 and n ≥ 4 .