Rational Classification of simple function space components for flag manifolds.

http://dx.doi.org/10.4153/CJM-1997-044-1
Canad. J. Math. 49(1997), 855-864

  Published:1997-08-01
 Printed: Aug 1997

Let $M(X,Y)$ denote the space of all continous functions between $X$ and $Y$ and $M_f(X,Y)$ the path component corresponding to a given map $f: X\rightarrow Y.$ When $X$ and $Y$ are classical flag manifolds, we prove the components of $M(X,Y)$ corresponding to ``simple'' maps $f$ are classified up to rational homotopy type by the dimension of the kernel of $f$ in degree two cohomology. In fact, these components are themselves all products of flag manifolds and odd spheres.