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# Rational Classification of simple function space components for flag manifolds.

Published:1997-08-01
Printed: Aug 1997
• Samuel Bruce Smith
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## Abstract

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.
 Keywords: Rational homotopy theory, Sullivan-Haefliger model.
 MSC Classifications: 55P62 - Rational homotopy theory 55P15 - Classification of homotopy type 58D99. - unknown classification 58D99.