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

DOI:
https://doi.org/10.1090/S0002-9947-1981-0626481-9

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0626481-9

Keywords:
Flag manifold,
homogeneous space,
rational homotopy,
self-map

Article copyright:
© Copyright 1981
American Mathematical Society