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k-Stability of homeomorphisms of Euclidean n-space

Published online by Cambridge University Press:  24 October 2008

W. R. Brakes
W. R. Brakes
Affiliation:
Department of Pure Mathematics, Cambridge University
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Extract

Kirby and Siebenmann (in (7)) proved the annulus conjecture in dimensions five and above, by proving the stable homeomorphism conjecture in those dimensions, that is, by proving that every orientation-preserving homeomorphism of Rn is stable, if n ≥ 5. Although this result apparently lessens the importance of stable homeomorphisms, the concept of stability should still be of use in settling the fate of the annulus conjecture in dimension 4, or for uncovering a simple (i.e. non-surgical) proof in other dimensions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 2 , March 1974 , pp. 175 - 183
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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