RATIONAL HOMOTOPY OF MAPPING SPACES BETWEEN COMPLEX GRASSMANNIANS

摘要

The complex Grassmann Gr(k, n) is the space of k dimensional subspaces of Double-struck capital C-n. It is a complex manifold of complex dimension k(n - k). There is a natural inclusion i(k,n) : Gr(k, n) x21aa; Gr(k, n + r). In this paper, we use Sullivan models to compute the rational homotopy type of the component of the inclusion Gr(2, n) x21aa; Gr(2, n + r) in the space of mappings from Gr(2, n) to Gr(2, n + r), r = 1. We show in particular that map(Gr(2, n), Gr(2, n + 1); i(n)) has the rational homotopy type of a product of odd spheres.