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On the h-enclosability of spheres†

Published online by Cambridge University Press:  24 October 2008

P. L. Antonelli
P. L. Antonelli
Affiliation:
University of Tennessee, Knoxville, Tennessee, U.S.A.
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Let Bk, Mn, Np be manifolds in the category C = Top, Duff or PL. Define Mn and Np to be h-enclosable in Bk if (1) k = n + p + 1, (2) there are C-imbeddings i:Mn ⊆ Bk and j: Np ⊆ Bk with disjoint images and (3) there are de formation retractions of Bk − i(Mn) onto j(Np) and of Bk − j(NP) onto i(Mn). This is expressed as Bk = [Mn, NP/i, j] (mod C). The manifolds are trivially h-enclosable in Bk if, in addition, each manifold has a product tubular neighbourhood in the category C.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 185 - 188
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Antonelli, P. L.On the stable diffeomorphism question of homotopy spheres in the stable range, n < 2p. Bull. Amer. Math. Soc. 75 (1969), 343–346.Google Scholar
(2)Haefliger, A. Plongements differentiables de varietes dans varietes. Comment. Math. Helv. 36 (1961), 155–176.Google Scholar
(3)Hsiang, W. C., Levine, J. and Szczarba, R. H.On the normal bundle of a homotopy sphere embedded in Euclidean space. Topology 3 (1965), 173–181.Google Scholar
(4)Kervaire, M. Aninterpretation of G. Whitehead's generalization of H. Hopf's invariant. Ann. of Math. (2) 69 (1956), 345–365.Google Scholar
(5)Kervajre, M. and Milnor, J.Groups of homotopy spheres: I. Ann. of Math. (3) 77 (1963), 504–537.Google Scholar
(6)Massey, W. Onthe normal bundle of a sphere imbedded in Eucidean space. Proc. Amer. Math. Soc. 10 (1959), 959–964.Google Scholar
(7)Milnor, J.Lectures on the h-cobordism theorem (Princeton Math Notes, 1965).Google Scholar
(8)Smale, S.On the structure of manifolds. Amer. J. Math. 84 (1962), 387–399.CrossRefGoogle Scholar
(9)Stallings, J.The piecewise linear structure of Euclidean space. Proc. Cambridge Philos. Soc. 58 (1962), 481–ndash;488.CrossRefGoogle Scholar
(10)Steenrod, N.Topology of fibre bundles (Princeton tTniversity Press, 1950).Google Scholar
(11)Wall, C. T. C.Unknotting Tori in codirnension one and spheres in codimension two. Proc. Cambridge Philos. Soc. 61 (1965), 659–664.CrossRefGoogle Scholar