Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T02:43:30.806Z Has data issue: false hasContentIssue false

The topological s-cobordism theorem fails in dimension 4 or 5

Published online by Cambridge University Press:  24 October 2008

T. Matumoto
Affiliation:
Kyoto University and Université de Paris-Sud, Orsay
L. Siebenmann
Affiliation:
Kyoto University and Université de Paris-Sud, Orsay

Extract

Although examples have been known since 1969 [Si], which reveal a quite similar failure of the differentiable and piecewise-linear s-cobordism theorems, these did not immediately suggest any topological failure.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1978

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

[Ce] Černavskii, A. V.Local contractibility of the homeomorphism group of a manifold. (Russian) Math. Sbornik 79 (1969), no. 121, 307356; (English) Math. U.S.S.R. Sbornik 8 (1969), no. 3, 287–333.Google Scholar
[EK] Edwards, R. D. and Kirby, R. C. Deformations of spaces of imbeddings. Ann. of Math. 93 (1971), 6388.CrossRefGoogle Scholar
[FH] Farrell, F. T. and Hsiang, W. C. Manifolds with ω1 = G × T. Amer. J. Math. 95 (1973), 813848.CrossRefGoogle Scholar
[Hi] Higman, G.The units of group rings. Proc. London Math. Soc. 46 (1940), 231248.CrossRefGoogle Scholar
[KS] Kirby, R. and Siebenmann, L.Foundational essays on topological manifolds. Ann. of Math. Study, no. 88 (1977).Google Scholar
[Mo] Moise, E.Affine structures on 3-manifolds. Ann. of Math. 56 (1952), 96114.CrossRefGoogle Scholar
[Sh] Shalen, P.A piecewise linear method for triangulating 3-manifolds. Preprint, Rice University, Houston, Texas, 1977.Google Scholar
[Si] Siebenmann, L. C. Disruption of low-dimensional handlebody theory by Rohlin's theorem. In Topology of manifolds, ed. Cantrell, J. C. and Edwards, C. H. (Athens Georgia Conf. 1969), pp. 5776 (Chicago, Markham, 1970).Google Scholar
[Wa] Wall, C. T. C.Surgery on compact manifolds (Academic Press, 1971).Google Scholar