Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians

Abstract

We consider the complex Grassmannian Grk,n of k-dimensional subspaces of n. There is a natural inclusion in,r:Grk,nGrk,n+r. Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion in,r in the space of mappings from Grk,n to Grk,n+r for r≥1 and in particular to show that the cohomology of mapGrn,k,Grn,k+r;in,r contains a truncated algebra x/xr+n+k2-nk, where x=2, for k≥2 and n≥4.