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A Generalization of Thom Classes and Characteristic Classes to Nonspherical Fibrations

Published online by Cambridge University Press:  20 November 2018

Reinhard Schultz
Reinhard Schultz*
Affiliation:
Purdue University, West Lafayette, Indiana
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Let X be a polyhedron, and let Fx denote the contravariant functor consisting of fiber homotopy types of Hurewicz fibrations over a given base whose fibers are homotopy equivalent to X. A fundamental theorem on fiber spaces states that Fx is a representable homotopy functor and a universal space for Fx is the classifying space for the topological monoid of self-equivalences of X [2; 5]. Frequently, algebraic topological information about the associated universal fibration yields information about arbitrary fibrations with fiber (homotopy equivalent to) X. However, present knowledge of the algebraic topological properties of the universal base space is extremely limited except in some special cases.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 138 - 144
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Conner, P. E. and Floyd, E. E., The relation of cobordism to K-theories, Lecture Notes in Mathematics, Vol. 28 (Springer, New York, 1966).Google Scholar
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3. Gottlieb, D. H., Applications of bundle map theory, Trans. Amer. Math. Soc. (to appear).Google Scholar
4. Gottlieb, D. H., Witnesses, transgressions, Hurewicz homomorphisms, and the evaluation map, mimeographed, Purdue University, 1971.Google Scholar
5. Stasheff, J., A classification theorem for fibre spaces, Topology 2 (1963), 239–246.Google Scholar