Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Self-maps of flag manifolds

Authors: Henry H. Glover and William D. Homer
Journal: Trans. Amer. Math. Soc. 267 (1981), 423-434
MSC: Primary 55P62; Secondary 14M17, 57T15
MathSciNet review: 626481
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Abstract: Rationally, a map between flag manifolds is seen to be determined up to homotopy by the homomorphism it induces on cohomology. Two algebraic results for cohomology endomorphisms then serve (a) to determine those flag manifolds which have (nontrivial) self-maps that factor through a complex projective space, and (b) for a special class of flag manifolds, to classify the self-maps of their rationalizations up to homotopy.

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Keywords: Flag manifold, homogeneous space, rational homotopy, self-map
Article copyright: © Copyright 1981 American Mathematical Society