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Local Spaces with Three Cells as H-Spaces

Published online by Cambridge University Press:  20 November 2018

Nancy L. Hagelgans
Nancy L. Hagelgans*
Affiliation:
Ursinus College, Collegeville, Pennsylvania Bryn Mawr College, Bryn Mawr, Pennsylvania
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The question of which finite CW-complexes are if-spaces has been studied for many years. Since a finite CW-complex is an H-space if and only if its localization at each prime p is an H-space [21], an examination of finite local cell complexes as H-spaces yields results concerning CW-complexes. On the other hand, if it is known that a particular CW-complex is not an H-space, one would like to know for which primes p its localization at p fails to be an H-space. The main result of this paper gives a condition equivalent to a three cell local CW-complex's being an H-space for a prime p > 3.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 6 , 01 December 1979 , pp. 1293 - 1306
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Adams, J. F., The sphere, considered as an H-space mod p, Quart. J. Math. Oxford (2). 12 (1961), 52–60.Google Scholar
2. Adams, J. F., H-spaces with few cells, Topology. 1 (1962), 67–72.Google Scholar
3. Cooke, G., Harper, J. and Zabrodsky, A., Torsion free mod p H-spaces of low rank, Preprint.Google Scholar
4. Curtis, M., H-spaces mod p (n), Lecture Notes in Mathematics 196 (Springer-Verlag, Berlin, 1970), 11–19.Google Scholar
5. Douglas, R. R. and Sigrist, F., Sphere bundles over spheres and H-spaces, Topology. 8 (1969), 115–118.Google Scholar
6. Harper, J., Private communication.Google Scholar
7. Hilton, P. J., On the homotopy groups of the union of spheres, J. London Math. Soc. 30 (1955), 154–172.Google Scholar
8. Hilton, P. J., Mislin, G., and Roitberg, J., Localization of nilpotent groups and spaces (North-Holland Publishing Company, Amsterdam-Oxford, 1975).Google Scholar
9. Hubbuck, J. R., Generalized cohomology operations and H-spaces of low rank, Trans. Amer. Math. Soc. 141 (1969), 335–360.Google Scholar
10. Hurewicz, W., On the concept of fiber space, Proc. Nat. Acad. Sci. 41 (1955), 956–961.Google Scholar
11. Kamber, F. W., Private communication.Google Scholar
12. James, I. M. and Whitehead, J. H. C., The homotopy theory of sphere bundles over spheres, I, Proc. London Math. Soc. (3). 4 (1954), 196–218.Google Scholar
13. James, I. M., Note on cup-products, Proc. Amer. Math. Soc. 8 (1957), 374–383.Google Scholar
14. Mimura, M., Nishida, G. and Toda, H., On the classification of H-spaces of rank 2, J. Math. Kyoto Univ. 13 (1973), 611–627.Google Scholar
15. Mislin, G., H-spaces mod p (I), Lecture Notes in Mathematics 196 (Springer-Verlag, Berlin, 1970), 5–10.Google Scholar
16. Sasao, S., Note on spaces with H*(; Z) = E[x1, x2], Kôdai Math. Sem. Rep. 27 (1976), 163–167.Google Scholar
17. Stasheff, J., A classification theorem for fiber spaces, Topology. 2 (1963), 239–246.Google Scholar
18. Stasheff, J., Sphere bundles over spheres as H-spaces mod p > 2, Lecture Notes in Mathematics 249 (Springer-Verlag, Berlin, 1971), 106–110.+2,+Lecture+Notes+in+Mathematics+249+(Springer-Verlag,+Berlin,+1971),+106–110.>Google Scholar
19. Sullivan, D., Genetics of homotopy theory and the Adams conjecture, Annals of Math. 100 (1974), 1–79.Google Scholar
20. Toda, H., Composition methods in homotopy groups of spheres, Annals of Math. Studies 49 Princeton (1962).Google Scholar
21. Zabrodsky, A., Hopf spaces (North-Holland Publishing Company, Amsterdam-Oxford, 1976).Google Scholar