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Constructing Locally Flat Embeddings of Infinite Dimensional Manifolds without Tubular Neighborhoods

Published online by Cambridge University Press:  20 November 2018

T. A. Chapman
T. A. Chapman*
Affiliation:
University of Kentucky, Lexington, Kentucky
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All spaces in this paper will be separable and metric. A closed embedding i: M → TV is said to be locally flat (of codimension n) if for each x0 ∈ M there is an open set U in M containing xo and an open embedding h: U X Rn → N for which h(x, 0) = i(x), for all x ∈ U.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1174 - 1182
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Brown, M., Locally flat embeddings of topological manifolds, Topology of 3-manifolds Prentice-Hall, (1962).Google Scholar
2. Chapman, T. A., nomotopic homeomorphisms of infinite-dimensional manifolds, Compositio Math. 27 (1973), 138–140.Google Scholar
3. Chapman, T. A., Lectures on Hilbert cube manifolds, C.B.M.S. Regional Conference Series in Math. 28, 1975.Google Scholar
4. Chapman, T. A. and Steve Ferry, Fibering Hilbert cube manifolds over ANRs, Compositio Math., 36 (1978), 7–35.Google Scholar
5. Chapman, T. A. and Wong, R. Y. T., On homeomorphisms of infinite-dimensional bundles, III, Trans. A.M.S. 101 (1974), 269–276.Google Scholar
6. Steve Ferry, The homeomorphism group of a compact Hilbert cube manifold is an ANR, Annals of Math., 106 (1977), 101–119.Google Scholar
7. Husemoller, D., Fiber bundles (McGraw-Hill, 1966).Google Scholar
8. Kirby, R. C. and Siebenmann, L. C., Normal bundles for codimension 2 locally flat embeddings, Proc. Topology Conf., Park City, Utah, Feb. 1974, Springer Lecture Notes in Math. 438, 1975.Google Scholar
9. Kirby, R. C. and Siebenmann, L. C., Foundational essays on topological manifolds, smoothings and triangulations, Annals of Math. Studies (Princeton University Press, 1977).Google Scholar
10. Milnor, J., Construction of universal bundles I, Annals of Math. 63 (1956), 272–284.Google Scholar
11. Milnor, J., Topological manifolds and smooth manifolds, Proc. Int. Cong. Math., Stockholm, 1962.Google Scholar
12. W\, Nowell, Locally flat“embeddings of Hilbert cube manifolds, Doctoral Dissertation, University of Kentucky, 1977.Google Scholar
13. Rourke, C. P. and Sanderson, B. J., An embedding without a normal microbundle, Invent. Math. 3 (1967), 293–299.Google Scholar
14. Stasheff, J., classification theorem for fiber spaces, Topology 2 (1963), 239–246.Google Scholar
15. Stern, Ronald J., On topological and piecewise linear vector fields, Topology 1J+ (1975), 257–269.Google Scholar
16. Wong, R. Y. T., On homeomorphisms of certain infinite-dimensional spaces, Trans. A.M.S. 128 (1967), 148–154.Google Scholar
17. Wong, R. Y. T., Parametric extensions of homeomorphisms on s-manifolds, Bull, of the Inst. Math. Academic Sinica 2 (1974), 121–126.Google Scholar