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Approximating Approximate Fibrations by Fibrations

Published online by Cambridge University Press:  20 November 2018

L. S. Husch
L. S. Husch*
Affiliation:
University of Tennessee, Knoxville, Tennessee 37916
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A map p: E → B between metric spaces has the approximate homotopy lifting property with respect to the space X if given a cover Ū of B and maps g: X → E and H: X × [0, 1] → B such that H(x, 0) = pg(x) for all x ϵ X, then there exists a map G: X × [0, 1] → E such that G(x, 0) = g(x) and pGt and Ht are Ū-close for all x ϵ X and t ϵ [0, 1]; i.e. given (x, t) ∊ X × [0, 1], there exists U × Ū such that pG(x, t) and H(x, t) are elements of U.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 897 - 913
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Anderson, R. D. and Chapman, T. A., Extending homeomorphisms to Hilbert cube manifolds, Pacific J. Math. 38 (1971), 281–293.Google Scholar
2. Armentrout, S., Cellular decompositions of 3-manifold s that yield 3-manifolds, Memoirs Am. Math. Soc. 107 (1971).Google Scholar
3. Borsuk, K., Theory of shape, Aarhus Universitet Matematisk Institut Lecture Notes Series, 28 (1971).Google Scholar
4. Brown, E. M., Unknotting in M2 A Trans. Am. Math. Soc. 123 (1966), 480–505.Google Scholar
5. Chapman, T. A., Surgery and handle straightening in Hilbert cube manifolds, Pacific J. Math. 45 (1973), 59–79.Google Scholar
6. Chapman, T. A. Compact Hilbert cube manifolds and the invariance of Whitehead torsion, Bull. Amer. Math. Soc. 79 (1973), 52–56.Google Scholar
7. Chapman, T. A. On the structure of Hilbert cube manifolds, Compositio Math. 24 (1972), 329–353.Google Scholar
8. Chapman, T. A. Notes on Hilbert cube manifolds, Am. Math. Soc. Regional Conf. Ser. (1975).Google Scholar
9. Chapman, T. A. All Hilbert cube manifolds are triangulable, (to appear).Google Scholar
10. Chapman, T. A. Simple homotopy theory for ANR's, (to appear).Google Scholar
11. Chapman, T. A. and Ferry, S., Hurewicz fiber ings of ANR's, (to appear).Google Scholar
12. Chapman, T. A. and Siebenmann, L. C., Finding a boundary for a Hilbert cube manifold, Acta Math. 137 (1976), 171–208.Google Scholar
13. Coram, D. S. and Duvall, P. F., Jr., Approximatefibrations, (to appear).Google Scholar
14. Coram, D. S. and Duvall, P. F. Approximate fibrations and a movability condition for maps, (to appear).Google Scholar
15. Edwards, C. H., Jr., Concentricity in 3-manifolds, Trans. Am. Math. Soc. 113 (1964), 406–423.Google Scholar
16. Edwards, R., (to appear).Google Scholar
17. Finney, R., Uniform limits of compact cell-like maps, Notices Am. Math. Soc, 15 (1968), 942.Google Scholar
18. Goad, R., Local homotopy properties of maps and approximation by fibre bundle projections, Thesis, University of Georgia, 1976.Google Scholar
19. Hempel, J. and Jaco, W., 3-manifolds which fiber over a surface, Amer. J. Math. 94 (1972), 189–205.Google Scholar
20. Hudson, J. F. P., Piecewise linear topology (W. A. Benjamin, Inc., 1969).Google Scholar
21. Husemoller, D., Fibre bundles (McGraw-Hill Book Co., 1966).Google Scholar
22. Husch, L. and Price, T., Finding a boundary for a 3-manij'old, Ann. Math. 91 (1970), 223–235.Google Scholar
23. Kirby, R. C. and Siebenmann, L. C., Essays on topological manifolds, smoothings and triangulations, (to appear).Google Scholar
24. Kirby, R. C. and Siebenmann, L. C. On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742–749.Google Scholar
25. Lâcher, R. C., Cell-like mappings I, Pacific J. Math. 30 (1969), 717–731.Google Scholar
26. Milnor, J., Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358–426.Google Scholar
27. Papakyriakopoulos, C., On solid tori, Proc. London Math. Soc. (3) 7 (1957), 281–299.Google Scholar
28. Siebenmann, L. C., The obstruction to finding a boundary for an open manifold of dimension greater than five, Thesis, Princeton University 1965.Google Scholar
29. Siebenmann, L. C. A total Whitehead torsion obstruction tofibering over the circle, Comm. Math. Helvetici 48 (1970), 1–48.Google Scholar
30. Siebenmann, L. C. Approximating cellular maps by homeomorphisms, Topology 11 (1973), 271–294.Google Scholar
31. Spanier, E. H., Algebraic topology (McGraw-Hill, 1966).Google Scholar
32. Stailings, J. R., On infinite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology (Princeton University Press, 1965), 245–254.Google Scholar
33. Wall, C. T. C., Finiteness conditions for CW-complexes, Ann. Math. 81 (1965), 56–59.Google Scholar