Abstract
In order to get results of non-embedding of flag-manifolds in the total space of sphere bundles we consider algebraic properties of these two families of manifolds.
The main theorem (2.3) gives a general a non-embedding result in terms of algebraic invariants and this theorem is applied to the case of the flag-manifolds.
Similar content being viewed by others
References
Atiyah, M. F. and F. Hirzebruch,Vector bundles and homogeneous spaces, Proceedings of the Symposia in Pure Mathematics, vol. 3, AMS (1961).
Bott, R.,A report on the unitary group, idem. Proceedings of the Symposia in Pure Mathematics, vol. 3, AMS (1961).
Borel, A. and F. Hirzebruch,Characteristic classes and homogeneous spaces, I, Amer. J. Math., 80 (1958).
Conde, A., B,genus and non-embeddings, PhD. Thesis, Chicago (1971).
Connell, F. J.,Non-immersions of spin and almost spin manifolds, PhD. Thesis, Chicago (1971).
Milnor, J. and J. D. Stasheff,Caracteristic classes Princeton University Press (1974).
Author information
Authors and Affiliations
About this article
Cite this article
do Patrocínio, A.C. Non embedding in sphere bundles. Bol. Soc. Bras. Mat 10, 1–14 (1979). https://doi.org/10.1007/BF02584626
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02584626