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The Map SJSF Does Not Deloop Mod 2

Published online by Cambridge University Press:  20 November 2018

Robert R. Clough*
Affiliation:
Burroughs Corporation, Chicago, Illinois
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It has been widely conjectured that there exists a homotopy commutative Diagram

where J is the stable Whitehead f-homomorphism and BSJ is the space constructed in [3]. In [4], Stasheff and the author proved that this conjecture is false. However, Quillen's proof of the Adams conjecture in [7] has as a corollary the existence of the homotopy commutative diagram

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Adams, J. F., On the groups J(X), IV, Topology 5 (1966), 2171.Google Scholar
2. Adams, J. F. and Walker, G., On Complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 61 (1965), 81103.Google Scholar
3. Clough, Robert R., T/je Z2-cohomology of a candidate for BImU), Illinois J. Math. 14 (1970), 424433.Google Scholar
4. Clough, Robert R. and Stasheff, James D., BSJ does not map correctly into BSF mod 2, Manuscripta Math. 7 (1972), 205214.Google Scholar
5. Milgram, R. J., Iterated loop spaces, Ann. of Math. 84 (1966), 386403.Google Scholar
6. Moore, J. C., Algebra homologique et homologie des espaces classifiants, Séminaire Henri Cartan, 19591960. Exp. 7.Google Scholar
7. Quillen, Daniel, The Adams conjecture (to appear).Google Scholar
8. Rothenberg, M. and Steenrod, N., The cohomology of classifying spaces of H-spaces, Bull. Amer. Math. Soc. 71 (1965), 872875.Google Scholar
9. Sullivan, Dennis, Geometric topology, I: Localization, periodicity, and Galois symmetry, M. I. T., Cambridge, Mass., 1970 (mimeographed notes).Google Scholar
10. Wu, W. T., Les i-carres dans une variété grassmannienne, C. R. Acad. Sci. Paris Sér. A-B 230 (1950), 918920.Google Scholar