Acta Mathematica

The Euler class of generalized vector bundles

J. Wolfgang Smith

Full-text: Open access


This research was supported in part by the National Science Foundation under NSF G-23722.


This revised version was published online in November 2006 with corrections to the Cover Date.

Article information

Acta Math., Volume 115 (1966), 51-81.

Received: 21 April 1965
First available in Project Euclid: 31 January 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

1966 © Almqvist & Wiksells Boktryckeri AB


Smith, J. Wolfgang. The Euler class of generalized vector bundles. Acta Math. 115 (1966), 51--81. doi:10.1007/BF02392202.

Export citation


  • Chevalley, C., Theory of Lie groups, I. Princeton University Press, 1946.
  • Clifton, Y. H. & Smith, J. W., The category of topological objects. Proc. Nat. Acad. Sci. U.S.A., 47 (1961), 190–195.
  • —, Topological objects and sheaves. Trans. Amer. Math. Soc., 105 (1962), 436–452.
  • —, The Euler class as an obstruction in the theory of foliations. Proc. Nat. Acad. Sci. U.S.A., 50 (1963), 949–954
  • Eilenberg, S., Singular homology theory. Ann. of Math., 45 (1944), 407–447.
  • Eilenberg, S., Foundations of fiber bundles. Lecture notes, University of Chicago, 1957.
  • Eilenberg, S. & Steenrod, N., Foundations of algebraic topology. Princeton University Press, 1952.
  • Godement, R., Théorie des faisceaux. Hermann, Paris, 1958.
  • Haefliger, A., Variétés feuilletées. Ann. Scuola Norm. Sup. Pisa, III, 106 (1962), 367–397.
  • Milnor, J., Lectures on characteristic classes. Notes by J. Stasheff, Princeton University, 1957.
  • Reeb, G., Sur certaines propriétés topologique des variétés feuilletées. Hermann, Paris, 1952.
  • Steenrod, N., The topology of fiber bundles. Princeton University Press, 1951.