On cohomology automorphisms of complex flag manifolds

Hoffman, Michael; Homer, William

doi:10.1090/S0002-9939-1984-0746106-X

On cohomology automorphisms of complex flag manifolds
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by Michael Hoffman and William Homer

Proc. Amer. Math. Soc. 91 (1984), 643-648

DOI: https://doi.org/10.1090/S0002-9939-1984-0746106-X

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Abstract:

We conjecture a classification of the automorphisms of the rational cohomology ring of $U\left ( n \right )/H$ for $H$ a closed connected subgroup of maximal rank in $U\left ( n \right )$, and prove a partial result.

References

Armand Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115–207 (French). MR 51508, DOI 10.2307/1969728
Stephen Brewster and William Homer, Rational automorphisms of Grassmann manifolds, Proc. Amer. Math. Soc. 88 (1983), no. 1, 181–183. MR 691305, DOI 10.1090/S0002-9939-1983-0691305-8
S. Allen Broughton, Michael Hoffman, and William Homer, The height of two-dimensional cohomology classes of complex flag manifolds, Canad. Math. Bull. 26 (1983), no. 4, 498–502. MR 716592, DOI 10.4153/CMB-1983-080-3
Henry H. Glover and William D. Homer, Self-maps of flag manifolds, Trans. Amer. Math. Soc. 267 (1981), no. 2, 423–434. MR 626481, DOI 10.1090/S0002-9947-1981-0626481-9
Henry H. Glover and Guido Mislin, On the genus of generalized flag manifolds, Enseign. Math. (2) 27 (1981), no. 3-4, 211–219 (1982). MR 659149
Michael Hoffman, Endomorphisms of the cohomology of complex Grassmannians, Trans. Amer. Math. Soc. 281 (1984), no. 2, 745–760. MR 722772, DOI 10.1090/S0002-9947-1984-0722772-4