Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-07-02T23:20:59.143Z Has data issue: false hasContentIssue false
  • English
  • Français

Embeddings of bounded manifolds

Published online by Cambridge University Press:  24 October 2008

J. F. P. Hudson
J. F. P. Hudson
Affiliation:
University of Durham
Get access Rights & Permissions [Opens in a new window]

Extract

Introduction. This paper gives some embedding and unknotting theorems for bounded manifolds in the PL and differential categories. The theorems are of a similar nature to the embedding and unknotting theorems of Irwin and Zeeman (9, 18), except that the boundaries are allowed to move and the appropriate connectivity conditions become conditions on the relative homotopy groups of the manifolds modulo the boundary, or some suitable part of the boundary.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 1 , July 1972 , pp. 11 - 20
Copyright
Copyright © Cambridge Philosophical Society 1972

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)Haefliger, A.Lissage des immersions. Topology 6 (1967), 221–240.CrossRefGoogle Scholar
(2)Haefliger, A.Plongements différentiables des variétés danas variétés. Comment. Math. Helv. 36 (1962), 47–82.CrossRefGoogle Scholar
(3)Hirsch, M. W.Smooth regular neighbourhoods. Ann. of Math. 76 (1962), 524–530.CrossRefGoogle Scholar
(4)Hirsch, M. W. and Zeeman, E. C.Engulfing. Bull. Amer. Math. soc. 72 (1966), 113–115.CrossRefGoogle Scholar
(5)Hudson, F. J. P. and Zeeman, E. C.On regular neighbourhoods. Proc. London Math. Soc. (3) 14 (1964), 719–745.CrossRefGoogle Scholar
(6)Hudson, J. F. P. and Zeeman, E. C. Correction to ‘On regular neighbourhoods’. Proc. London Math. Soc. (31), 21 (1970), 513–524.CrossRefGoogle Scholar
(7)Hudson, J. F. P.Concordance and isotopy of PL embeddings. Bull. Amer. Math. Soc. 72 (1966), 534–535.CrossRefGoogle Scholar
(8)Hudson, J. F. P.Concordance isotopy and diffeotopy. Ann. of Math. 91, 3 (1970), 425–448.CrossRefGoogle Scholar
(9)Irwin, M. C.Embeddings of polyhedral manifolds. Ann. of Math. 82, 1 (1965), 1–14.CrossRefGoogle Scholar
(10)Lashof, R. and Rothenberg, M.Microbundles and smoothing. Topology 3 (1965), 357–388.CrossRefGoogle Scholar
(11)Munkres, J. R. Elementary differential topology. Ann. of Math. Studies, no. 54 (Princeton University Press, 1963).Google Scholar
(12)Penrose, R., Whitehead, J. H. C. and Zeeman, E. C.Imbedding manifolds in Euclidean space. Ann. of Math. 73 (1961), 613–623.CrossRefGoogle Scholar
(13)Siebenman, L. C. Doctoral dissertation, Princeton University, 1965.Google Scholar
(14)Wall, C. T. C.Classification problems in differential topology IV. Thickenings. Topology 5 (1966), 73–94.CrossRefGoogle Scholar
(15)Whitehead, J. H. C.On C1 complexes. Ann. of Math. 41 (1940), 809–814.CrossRefGoogle Scholar
(16)Whitney, H.The self intersections of a smooth n–manifold in 2n–space. Ann. of Math. 45 (1944), 247–293.CrossRefGoogle Scholar
(17)Zeeman, E. C.Seminar on combinatorial Topology, Mineographed notes I.H.E.S., 1963.Google Scholar
(18) Zeeman, E. C. Isotopies and knots in manifolds: Topology of 3-manifolds, ed. Fort, M. K.. (Prentice Hall, 1962).Google Scholar
(19)Hudson, J. F. P.Piecewise linear topology (Benjamin, 1969).Google Scholar
(20)Whitehead, H. H. C.Simplicial spaces nuclei and m–groups. Proc. London Math. Soc. 45 (1939), 243–327.CrossRefGoogle Scholar
(21)Wall, C. T. C.All 3-manifolds imbed in 5-space. Bull. Amer. Math. Soc. 71 (1965), 564–567.CrossRefGoogle Scholar
(22)Connelly, R.A new proof of Brown's Collaring Theorems. Proc. Amer. Math. Soc. 27, 1 (1971), 180–182.Google Scholar