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The Height of Two-Dimensional Cohomology Classes of Complex Flag Manifolds

Published online by Cambridge University Press:  20 November 2018

S. Allen Broughton ,
Michael Hoffman  and
William Homer
S. Allen Broughton
Affiliation:
Memorial University of NfldSt. Johns, Newfoundland, Canada, A1B3X7
Michael Hoffman
Affiliation:
Memorial University of NfldSt. Johns, Newfoundland, Canada, A1B3X7
William Homer
Affiliation:
Memorial University of NfldSt. Johns, Newfoundland, Canada, A1B3X7
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Abstract

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For a parabolic subgroup H of the general linear group G = Gl(n, C), we characterize the Kähler classes of G/H and give a formula for the height of any two-dimensional cohomology class. As an application, we classify the automorphisms of the cohomology ring of G/H when this ring is generated by two-dimensional classes.

Keywords

57T15Secondary 53C55Flag manifoldheightKähler manifold
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 4 , 01 December 1983 , pp. 498 - 502
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Borel, A., Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. 57 (1953), 115-207.Google Scholar
2. Ewing, J. and Liulevicius, A., Homotopy rigidity of linear actions on homogeneous spaces, J. of Pure and Applied Alg. 18 (1980), 259-267.Google Scholar
3. Glover, H. and Mislin, G., On the genus of generalized flag manifolds, Enseign. Math. XXVII (1981), 211-219.Google Scholar
4. Griffiths, P. and Harris, J., Principles of Algebraic Geometry, Wiley, New York, 1978.Google Scholar
5. Liulevicius, A., Homotopy rigidity of linear actions: characters tell all, Bull. AMS 84 (1978), 213-221.Google Scholar
6. Monk, J. D., Geometry of flag manifolds, Proc. London Math. Soc. (3) 9 (1959) 253-286.10.1112/plms/s3-9.2.253Google Scholar
7. Wells, R. O., Differential Analysis on Complex Manifolds. Springer-Verlag, New York, 1980.Google Scholar