Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-17T14:39:17.310Z Has data issue: false hasContentIssue false
  • English
  • Français

Bundle structures on manifolds

Published online by Cambridge University Press:  24 October 2008

J. B. Wagoner
J. B. Wagoner
Affiliation:
Department of Mathematics, Fine Hall, Princeton University, Princeton, N.J., U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

This note gives homotopy-theoretic criteria in the metastable range for an (n + l)-manifold with boundary to be diffeomorphic to the total space of an l-disc bundle over a closed n-manifold and for two such structures to be equivalent. The results are similar to some theorems of (8) and the main technique used in the proofs is surgery on a map ((l), pp. 42–46, (7), (10)). All manifolds will be smooth.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 1 , January 1966 , pp. 19 - 22
Copyright
Copyright © Cambridge Philosophical Society 1966

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

REFERENCES

(1)Browder, W. Homotopy type of differentiable manifolds. Colloquium of Algebraic Topology (Aarhus, 1962).Google Scholar
(2)Brown, E. H. Jr and Peterson, F. P.The Kervaire invariant of (8K + 2)-manifolds. Bull. Amer. Math. Soc. 71 (1965), 190–193.CrossRefGoogle Scholar
(3)Haefliger, A.Knotted (4K − 1) spheres in 6K-space. Ann. of Math. (2) 75 (1962), 452–466.CrossRefGoogle Scholar
(4)Hirsch, M. W.Smooth regular neighborhoods. Ann. of Math. (2), 76 (1962), 524–530.CrossRefGoogle Scholar
(5)Hirsch, M. W.On the fibre homotopy type of normal bundles of manifolds, mimeographed notes, Cambridge Univ., Cambridge, England.Google Scholar
(6)Kervaire, M. and Milnor, J.Groups of homotopy spheres, I. Ann. of Math. (2), 77 (1963), 504–537.CrossRefGoogle Scholar
(7)Lashof, R.Some theorems of Browder and Novikov on homotopy equivalent manifolds with applications, printed notes, Univ. of Chicago, Chicago, Illinois.Google Scholar
(8)Levine, J.On differentiable imbeddings of simply connected manifolds. Bull. Amer. Math. Soc. 69 (1963), 806–809.CrossRefGoogle Scholar
(9)Milnor, J.Differential topology, mimeographed notes (1958), Princeton Univ., Princeton N.J.Google Scholar
(10)Wall, C. T. C.An extension of results of Novikov and Browder, mimeographed notes. Cambridge Univ., Cambridge, England.CrossRefGoogle Scholar
(11)Wall, C. T. C.Differential topology, mimeographed notes, Cambridge Univ., Cambridge, England.CrossRefGoogle Scholar