Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Nonimmersions of flag manifolds


Author: S. A. Ilori
Journal: Proc. Amer. Math. Soc. 61 (1976), 141-144
MSC: Primary 14M15; Secondary 57D40
DOI: https://doi.org/10.1090/S0002-9939-1976-0424840-4
MathSciNet review: 0424840
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Certain useful quadratic identities in the cohomology of classifying spaces induce quadratic equations in the cohomology of a manifold $ M$ under the classifying map for the normal bundle of $ M$. In low dimensional flag manifolds, one can show that the quadratic equation has no root, thus establishing a nonimmersion.


References [Enhancements On Off] (What's this?)

  • [1] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538. MR 21 #1586. MR 0102800 (21:1586)
  • [2] Fred J. Connell, Nonimmersions of low dimensional flag manifolds, Proc. Amer. Math. Soc. 44 (1974), 474-478. MR 49 #8037. MR 0343295 (49:8037)
  • [3] M. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242-276. MR 22 #9980. MR 0119214 (22:9980)
  • [4] F. Hirzebruch, Topological methods in algebraic geometry, 3rd ed., Springer-Verlag, Berlin and New York, 1966. MR 34 #2573. MR 0202713 (34:2573)
  • [5] W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry, Vol. II, Cambridge Univ. Press, New York, 1952. MR 13, 972. MR 1288306 (95d:14002b)
  • [6] S. A. Ilori, Canonical systems on flag manifolds, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 17 (1974), 10-17. MR 0405448 (53:9241)
  • [7] Séminaire C. Chevalley, 2e année, Anneaux de Chow et applications, Secrétariat math., Paris, 1958. MR 22 #1572.
  • [8] J. Tornehave, Immersions of complex flag manifolds, Math. Scand. 23 (1968), 22-26 (1969). MR 40 #4970. MR 0251743 (40:4970)
  • [9] E. Vesentini, Construction géométrique des classes de Chern de quelques variétés de Grassmann complexes, Colloque de topologie algébrique, Louvain, 1956, 97-120; Thone, Liège; Masson, Paris, 1957. MR 21 #1585. MR 0102799 (21:1585)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14M15, 57D40

Retrieve articles in all journals with MSC: 14M15, 57D40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0424840-4
Keywords: Normal bundle, Chern class, Pontryagin class, Euler class, classifying space
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society