Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T13:53:34.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Locally flat PL submanifolds with codimension two

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
C. T. C. Wall
Affiliation:
University of Liverpool
Get access Rights & Permissions [Opens in a new window]

Extract

We refer the reader to the IHES notes of Zeeman (14) for basic facts about PL (or piecewise-linear) manifolds. If Mm is a locally flat PL-submanifold of Qm+2, our object will be to study the normal structure of M in Q: one of our main results is:

There exists a PL-bundle over M, with fibre a 2-simplex, which is PL-homeomorphic to a neighbourhood of M in Q; moreover, the bundle and homeomorphism are unique up to equivalence. We also make an application to smoothing theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 5 - 8
Copyright
Copyright © Cambridge Philosophical Society 1967

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)Cerf, J.La nullité du group Γ4. Sim H. Carton, Paris, 1962/1963, no. 10.Google Scholar
(2)Haefliger, A. Smoothing immersions (to appear).Google Scholar
(3)Haefliger, A. and Wall, C. T. C.Piecewise linear bundles in the stable range. Topology 4 (1965), 209–214.CrossRefGoogle Scholar
(4)Hirsch, M. W.On combinatorial submanifolds of differentiable manifolds. Comment. Math. Helv. 36 (1962), 108–111.CrossRefGoogle Scholar
(5)Hirsch, M. W.Smooth regular neighbourhoods. Ann. of Math. 76 (1962), 524–530.CrossRefGoogle Scholar
(6)Hudson, J.Extending isotopies. Proc. London Math. Soc. 16 (1966), 651–668.CrossRefGoogle Scholar
(7)Kuiper, N. and Lashof, R. K.Microbundles and bundles. Inventiones Mathematicae 1 (1966), 1–17.CrossRefGoogle Scholar
(8)Lashof, R. K. and Rothenberg, M.Microbundles and smoothing. Topology 3 (1965), 357–388.CrossRefGoogle Scholar
(9)Massey, W. S.On the normal bundle of a sphere embedded in Euclidean Space. Proc. Amer. Math. Soc. 10 (1959), 959–964.CrossRefGoogle Scholar
(10)Smale, S.Diffeomorphisms of the 2-sphere. Proc. Amer. Math. Soc. 10 (1959), 621–626.CrossRefGoogle Scholar
(11)Stallings, J.On topologically unknotted spheres. Ann. of Math. 77 (1963), 490–503.CrossRefGoogle Scholar
(12)Wall, C. T. C.Unknotting tori in codimension one and spheres in codimension two. Proc. Cambridge Philos. Soc. 61 (1965), 659–664.CrossRefGoogle Scholar
(13)Whitehead, J. H. C.On C-triangulations. Ann. of Math. 41 (1940), 809–824.CrossRefGoogle Scholar
(14)Zeeman, E. C.Seminar on Combinatorial Topology. Institut des Hautes Études Scientifiques, 1963.Google Scholar
(15)Hirsch, M. W. and Mazur, B.Smoothings of Piecewise Linear Manifolds. Mimeographed, Cambridge University, 1964.Google Scholar
(16)Mazur, B.Séminaire de Topologie Combinatoire et Différentielle de l' Institut des Hautes Études Scientifiques, 1962–1963.Google Scholar