Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T02:21:18.094Z Has data issue: false hasContentIssue false
  • English
  • Français

Bundles of Grassmannians and integrality theorems

Published online by Cambridge University Press:  24 October 2008

R. S. Roberts
R. S. Roberts
Affiliation:
Department of Pure Mathematics, University of Liverpool
Get access Rights & Permissions [Opens in a new window]

Extract

Introduction. For applications in differential topology it is desirable to be able to find restrictions on the possible real and complex vector bundles over a given manifold. These restrictions usually state that the top component of some specific rational multinomial in the various characteristic classes is an integral multiple of the fundamental cocycle. For example, in proving non-embedding or non-immersion theorems (compare (1); (10)) one could test whether the normal bundle is consistent with these integrality conditions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 45 - 53
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Atiyah, M. F. and Hirzebruch, F.Quelques théorèmes de non-plongement pour les variétés difftérentiables. Bull. Soc. Math. France 87 (1959), 383–396.Google Scholar
(2)Atiyah, M. F. and Hirzebruch, F.Riemann–Roch theorems for differentiable manifolds. Bull. Amer. Math. Soc. 65 (1959), 276–281.CrossRefGoogle Scholar
(3)Atiyah, M. F. and Singer, I. M.The index of elliptic operators on compact manifolds. Bull. Amer. Math. Soc. 69 (1963), 422–433.CrossRefGoogle Scholar
(4)Borel, A. and Hirzebruch, F.Characteristic classes and homogeneous spaces, I. II, and III. Amer. J. Math. 80 (1958), 458–538; 81 (1959), 315–382; 82 (1960), 491–504.CrossRefGoogle Scholar
(5)Grothendieck, A.La théorie des classes de Chern. Bull. Soc. Math. France 86 (1958), 137–154.Google Scholar
(6)Hirzebruch, F.Topological methods in algebraic geometry, third edition (Berlin-Heidelberg-New York: Springer-Verlag, 1966)Google Scholar
(7)Mayer, K. H.Elliptische differentialoperatoren und ganzzahligkeitssätze für charakteristische zahlen. Topology 4 (1965), 295–313.CrossRefGoogle Scholar
(8)Palais, R. S.Seminar on the Atiyah-Singer index theorem (Annals of Mathematics Studies, 1965).Google Scholar
(9)Robertson, S. A. and Schwarzenberger, R. L. E.Vector bundles that fill n-space. Proc. Cambridge Philos. Soc. 61 (1965), 869–875.CrossRefGoogle Scholar
(10)Sanderson, B. J. and Schwarzenberger, R. L. E.Non-immersion theorems for differentiable manifolds. Proc. Cambridge Philos. Soc. 59 (1963), 319–322.CrossRefGoogle Scholar