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Some embeddings of projective spaces

  • I. M. James (a1)

1. Introduction. We say that a smooth compact manifold is embedded in q–space when there is given a regular one-one map of the manifold into q–dimensional Euclidean space. Whitney (5) has shown that embeddings always exist when q is not less than twice the dimension of the manifold.

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(1)Freudenthal, H.Zur Ebene Octavengeometrie. Indag. Math. 15 (1953), 195200.
(2)Hopf, H.Systeme symmetriBcher Bilinearformen und euklidische Modelle der projectiven Raüme. Vierteljschr. naturf. Ges. Zürich, 85 (1940), 165–77.
(3)Massey, W. S.On the cohomology ring of a sphere bundle. J. Math. Mech. 7 (1958), 265–90.
(4)Thom, R.Espaces fibrés en sphères et carres de Steenrod. Ann. Éc. Norm. (3), 69 (1952), 109–82.
(5)Whitney, H.The self-intersections of a smooth n–manifold in 2n–spaoe. Ann. Math., Princeton, 45 (1944), 220–46.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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