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Double Covers and Metastable Immersions of Spheres

Published online by Cambridge University Press:  20 November 2018

Robert Wells
Robert Wells*
Affiliation:
Pennsylvania State University, University Park, Pennsylvania
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The real line will be R, Euclidean n-space will be Rn, the unit ball in Rn will be En, the unit sphere in Rn+1 will be Sn, and real projective n-space will be Pn. The canonical line bundle associated with the double cover Sn → Pn will be ηn. If γ is a vector bundle, E(γ) will be its associated cell bundle, S(γ) its associated sphere bundle, P(γ) its associated projective space bundle (P(γ) = S(γ) / (-1)) and T(γ) = E(γ)/S(γ) its Thorn space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 145 - 176
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Conner, P. E. and Floyd, E. E., Fixed point free involutions and equivariant maps, Bull. Amer. Math. Soc. 66 (1960), 416–441 ; and 105 (1962), 222–228.Google Scholar
2. Connolly, F., From immersions to embeddings of smooth manifolds, Trans. Amer. Math. Soc. 152 (1970), 253–271.Google Scholar
3. Haefliger, A., Plongements differentiates de variétés dans variétés, Comment. Math. Helv. 36 (1961), 47–82.Google Scholar
4. Haefliger, A., Plongements differentiates dans le domaine stable, Comment. Math. Helv. 37 (1962/63), 155–176.Google Scholar
5. Kervaire, M. A., A manifold which does not admit any differentiable structure, Comment. Math. Helv. 34 (1960), 257–270.Google Scholar
6. Miller, J. G., Self-intersections of some immersed manifolds, Trans. Amer. Math. Soc. 136 (1969), 329–338.Google Scholar
7. Schneider, H., Free involutions on homotopy S[h/2] × Sh-[h/2] s , Ph.D. Thesis, University of Chicago, 1972.Google Scholar
8. Schweitzer, P. A., Joint cob ordism of immersions, The Steenrod algebra and its applications: A conference to celebrate N. E. Steenrod's sixtieth birthday. Proceedings of the conference held at the Batelle Memorial Institute (Springer-Verlag, 1972).Google Scholar
9. Uchida, F., Exact sequences involving cobordism groups of immersions, Osaka J. Math. 6 (1969), 397–408.Google Scholar
10. Wells, R., Cobordism groups of immersions, Topology 5 (1966), 281–294.Google Scholar
11. Wells, R., Modification of intersections, Illinois Math. 11 (1967), 389–399.Google Scholar
12. Wells, R., Some examples of free involutions on homotopy Sl × Sl's , Illinois J. Math. 15 (1971), 542–550.Google Scholar
13. Wells, R., Free involutions of Homotopy Sl × Sl's , Illinois Math. 15 (1971), 160–184.Google Scholar