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A topology on the space of PL homeomorphisms of a PL manifold

Published online by Cambridge University Press:  24 October 2008

Anthony Smith
Anthony Smith
Affiliation:
Queen's University, Belfast
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Extract

0. Introduction. It has long been known that the space of all smooth homeomorphisms of a smooth manifold with the Cl topology can be given the structure of a smooth manifold. A path in this space corresponds to a diffeotopy. It has been shown more recently (1) that the space of all homeomorphisms of a topological manifold is locally contractible when given the C–0 topology. A path in this space corresponds to an isotopy.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 3 , November 1974 , pp. 497 - 502
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Černavskii, A. V.Local contractibility of the Homeomorphism Group of a Manifold: Doklady 9 (1968), 1171–1174; and Mat. USSR Sb 8 (1969), 287–333.Google Scholar
(2)Haefliger, A.Lissage des Immersions I: Topology 6 (1967), 221–239.CrossRefGoogle Scholar
(3)Hirsch, M. W.Obstruction theories for smoothing manifolds and maps: Bull. Amer. Math. Soc. 69 (1963), 352–356.Google Scholar
(4)Kirby, R. C.Topological manifolds: Graduate Lecture Course. Cambridge, 1969.Google Scholar
(5)Whitehead, J. H. C.On Cl complexes: Ann. of Math. 41 (1940), 809–824.CrossRefGoogle Scholar
(6)Lashof, R. The immersion approach to triangulation: in Topology of manifolds (Markham Publishing Co.).Google Scholar
(7)Rourke, C. P. Embedded handlebody theory, concordance and isotopy: ibidem.Google Scholar
(8)Zeeman, E. C.Seminar on combinatorial topology: I.H.E.S. 1963.Google Scholar