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Non-embeddings of the real flag manifolds RF (1, 1, n – 2)

Part of: Differential topology

Published online by Cambridge University Press:  09 April 2009

Deborah O. Ajayi  and
Samuel A. Ilori
Deborah O. Ajayi
Affiliation:
Department of Mathematics, University of Ibadan, Ibadan, Nigeria
Samuel A. Ilori
Affiliation:
Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana e-mail: ilorisa@noka. ub. bw
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Abstract

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This paper gives non-embeddings and non-immersions for the real flag manifolds RF(1, 1, n–2), n > 3 and shows that Lam's immersions for n = 4 and 5 and Stong's result for n = 6 are the best possible.

MSC classification

Secondary: 57R20: Characteristic classes and numbers 57R40: Embeddings 57R42: Immersions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 1 , February 1999 , pp. 51 - 55
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Borel, A., ‘La cohomologie mod 2 de certains escapes homogènes’, Comment. Math. Helv. 27 (1953), 165–197.CrossRefGoogle Scholar
[2]Borel, A. and Hirzebruch, F., ‘Characteristic classes and homogeneous spaces’, Amer J. Math.: I, 80 (1958), 459–538; II, 81 (1959), 315–382; III, 82 (1960), 491–504.CrossRefGoogle Scholar
[3]Hiller, H. and Stong, R. E., ‘Immersion dimension for real Grassmannians’, Math. Ann. 225 (1981), 361–367.CrossRefGoogle Scholar
[4]Lam, K. Y., ‘A formula for the tangent bundle of flag manifolds and related manifolds’, Trans. Amer. Math. Soc. 213 (1975), 305–314.CrossRefGoogle Scholar
[5]Milnor, J. and Stasheff, J., Characteristic classes, Ann. of Math. Stud. 76 (Princeton Univ. Press, Princeton, 1974).CrossRefGoogle Scholar
[6]Oproiu, V., ‘Some non-embedding theorems for the Grassmann manifolds G 2.n and G 3.n’, Proc. Edinburgh Math. Soc. 20 (1976), 177–185.CrossRefGoogle Scholar
[7]Sanderson, B. J., ‘Immersions and embeddings of projective spaces’, Proc. London Math. Soc. 14 (1964), 137–153.CrossRefGoogle Scholar
[8]Steenrod, N., The topology of fibre bundles (Princeton Univ. Press, Princeton, 1951).CrossRefGoogle Scholar
[9]Stong, R. E., ‘Immersions of real flag manifolds’, Proc. Amer. J. Math. 88 (1983), 708–710.CrossRefGoogle Scholar
[10]Thomas, E., ‘On tensor products of n-plane bundles’, Arch. Math. 10 (1959), 174–179.CrossRefGoogle Scholar
[11]Whitney, H., ‘The self-intersection of a smooth manifold in 2n-space’, Ann. of Math. 45 (1944), 220–246.CrossRefGoogle Scholar
[12]Whitney, H., ‘The singularities of a smooth n-manifold in (2n – 1)-space’, Ann. of Math. 45 (1944), 248–293.Google Scholar