Rational Classification of simple function space components for flag manifolds.
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.
Rational homotopy theory, Sullivan-Haefliger model.
55P62 - Rational homotopy theory
55P15 - Classification of homotopy type
58D99. - unknown classification 58D99.