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Rational Classification of Simple Function Space Components for Flag Manifolds

Published online by Cambridge University Press:  20 November 2018

Samuel Bruce Smith
Samuel Bruce Smith*
Affiliation:
Department of Mathematics, St. Joseph's University, Philadelphia, PA 19131 e-mail: smith@sju.edu
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Abstract

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LetM(X, Y) denote the space of all continuous functions between X and Y and Mƒ(X, Y) the path component corresponding to a given map ƒ : X → Y. When X and Y are classical flag manifolds, we prove the components of M(X, Y) corresponding to “simple” maps ƒ are classified up to rational homotopy type by the dimension of the kernel of ƒ in degree two cohomology. In fact, these components are themselves all products of flag manifolds and odd spheres.

Keywords

55P6255P1558D99Rational homotopy theorySullivan-Haefliger model
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 855 - 864
Copyright
Copyright © Canadian Mathematical Society 1997

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