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Thin Lens Spaces

Published online by Cambridge University Press:  20 November 2018

P. Hoffman
Affiliation:
University of Waterloo, Waterloo, Ontario, Canada
A. Zabrodsky
Affiliation:
The Hebrew University, Jerusalem
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In Theorem 1 below we study the existence of spaces whose cohomology rings are isomorphic (as ungraded rings) to those of lens spaces. The case p = 2 is very simple and instructive, so let us consider it first.

Suppose X is a space such that where dim x = 2d (for example X = RP4 with d = 1).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Adams, J. F.: Lecture 4, Splitting Generalized Cohomology Theories with coefficients, in Category Theory, Homology Theory and their Applications III, Springer Lecture Notes in Mathematics, Vol.99. Google Scholar
2. Adams, J. F.: The Kahn-Priddy Theorem, Proc. Comb. Phil. Soc. 73 (1973), 45-55.Google Scholar
3. Atiyah, M. F.: Power Operations in K-theory, Quart. J. Math. Oxford (2), 17 (1966), 165-93.Google Scholar
4. Atiyah, M. F. and Tall, D. O.: Group Representations, À -Rings and the J-Homomorphism, Topology 8 (1969), 253-97.Google Scholar
5. Zabrodsky, A.: On the category of endomorphisms of finite complexes (to appear).Google Scholar