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Projective Homotopy Classes of Stiefel Manifolds

Published online by Cambridge University Press:  20 November 2018

Joseph Strutt
Joseph Strutt*
Affiliation:
Tulane University, New Orleans, Louisiana
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Given a homotopy class [f] in πn(X), we say that [f] is projective if and only if there is a homotopy commutative factorization

where v is the standard double covering. We then denote by the subset of projective homotopy classes in πn(X).

The notion of projective homotopy classes was studied in the author's thesis [5], and the projective homotopy classes for spheres in the stable range, up through the 3-stem were calculated in [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 3 , June 1972 , pp. 465 - 476
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Mosher, R. E. and Tangora, M. C., Cohomology operations and applications in homotopy theory (Harper and Row, New York, 1966).Google Scholar
2. Paechter, G. F., The groups πr(Vm,n)(I), Quart. J. Math. Oxford Ser. 7 (1956), 249–268.Google Scholar
3. Spanier, E. H., Algebraic topology (McGraw-Hill, New York, 1968).Google Scholar
4. Steenrod, N. and Epstein, D. B. A., Cohomology operations, Annals of Mathematics Studies 50 (Princeton University Press, Princeton, 1962).Google Scholar
5. Strutt, J. R. A., Projective homotopy classes, Ph.D. thesis, University of Illinois, 1970.Google Scholar
6. Strutt, J. R. A., Projective homotopy classes of spheres in the stable range (to appear in Bol. Soc. Mat. Mex.).Google Scholar
7. Zvengrowski, P., Skew linear vector fields on spheres, J. London Math. Soc. 3 (1971), 625–632.Google Scholar