Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T14:24:33.784Z Has data issue: false hasContentIssue false
  • English
  • Français

Unknotting tori in codimension one and spheres in codimension two

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
C. T. C. Wall
Affiliation:
Mathematical Institute, Oxford
Get access Rights & Permissions [Opens in a new window]

Extract

We shall present this paper in the framework and terminology of differential topology though all our arguments are valid in the piecewise linear ease also, under local un-knottedness hypotheses. In particular we use Rp for Euclidean space of dimension p, Sp−1 for the standard unit sphere in it, and Dp for the disc which it bounds.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 3 , July 1965 , pp. 659 - 664
Copyright
Copyright © Cambridge Philosophical Society 1965

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

(1)Alexander, J. W.On the subdivision of 3-spaco by a polyhedron. Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 6–8.CrossRefGoogle ScholarPubMed
(2)Barden, D. To appear.Google Scholar
(3)Epstein, D. B. A.Linking spheres. Proc. Cambridge Philos. Soc. 56 (1960), 215–219.CrossRefGoogle Scholar
(4)Kervaire, M. A. and Milnor, J. W.Groups of homotopy spheres I. Ann. of Math. 77 (1963), 504–537.CrossRefGoogle Scholar
(5)Kosinski, A. On Alexander's Theorem and Knotted Spheres. Topology of 3-manifolds and related topics (Prentice-Hall, 1962), pp. 55–57.Google Scholar
(6)Levine, J. Unknotting homology spheres in codimension two. To appear in Topology.Google Scholar
(7)Smale, S.On the structure of manifolds. American J. Math. 84 (1962), 387–399.CrossRefGoogle Scholar
(8)Wall, C. T. C.Killing the middle homotopy groups of odd dimensional manifolds. Trans. American Math. Soc. 103 (1962), 412–433.CrossRefGoogle Scholar
(9)Wall, C. T. C.Differential topology IV, mimeographed (Cambridge, 1964).Google Scholar
(10)Whitney, H.Differentiable manifolds. Ann. of Math. 37 (1936), 645–680.CrossRefGoogle Scholar
(11)Wu, W. T.On the isotopy of Cr-manifolds of dimension n in Euclidean (2n + l)-space. Sci. Record N.S. 2 (1958), 271–275.Google Scholar