Degrees of Maps between complex Grassmann Manifolds[HBNI Th16]

Abstract

Let f:Gn,k --> Gm,l be any continuous map between to distinct complex ( resp. quaternionic )Grassmann manifolds of the same dimension. It is shown that the degree of f is zero provided n, m are sufficiently large and l > or = 2. If the degree of f is + or - 1, it is shown that(m,l) + (n,k) and f is a homotopy equivalence. Also it is proved that the image under f* of elements of a set of algebra generators of H*(Gm,l ; Q)is determined upto a sign, + or -, if the degree of f is non-zero.