## Approximate torus fibrations of high dimensional manifolds can be approximated by torus bundle projections

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- by R. E. Goad PDF
- Trans. Amer. Math. Soc.
**258**(1980), 87-97 Request permission

## Abstract:

In this paper, we prove that approximate torus fibrations of high dimensional manifolds can be approximated by torus bundle projections. The principal tools are the torus trick developed by Kirby and Siebenmann, a surgery theorem concerning homotopy structures on torii due to Hsiang and Wall, a theorem on the space of homeomorphisms of the torus due to Hamstrom and a generalization of hereditary homotopy equivalence developed by the author.## References

- D. S. Coram and P. F. Duvall Jr.,
*Approximate fibrations*, Rocky Mountain J. Math.**7**(1977), no.Β 2, 275β288. MR**442921**, DOI 10.1216/RMJ-1977-7-2-275 - Donald Coram and Paul Duvall,
*Approximate fibrations and a movability condition for maps*, Pacific J. Math.**72**(1977), no.Β 1, 41β56. MR**467745** - T. A. Chapman and Steve Ferry,
*Hurewicz fiber maps with ANR fibers*, Topology**16**(1977), no.Β 2, 131β143. MR**448356**, DOI 10.1016/0040-9383(77)90011-8
β, - E. Dyer and M.-E. Hamstrom,
*Completely regular mappings*, Fund. Math.**45**(1958), 103β118. MR**92959**, DOI 10.4064/fm-45-1-103-118 - F. T. Farrell, L. R. Taylor, and J. B. Wagoner,
*The Whitehead theorem in the proper category*, Compositio Math.**27**(1973), 1β23. MR**334226**
R. E. Goad, - Mary-Elizabeth Hamstrom,
*The space of homeomorphisms on a torus*, Illinois J. Math.**9**(1965), 59β65. MR**170334** - L. S. Husch,
*Approximating approximate fibrations by fibrations*, Canadian J. Math.**29**(1977), no.Β 5, 897β913. MR**500990**, DOI 10.4153/CJM-1977-091-2 - W.-c. Hsiang and C. T. C. Wall,
*On homotopy tori. II*, Bull. London Math. Soc.**1**(1969), 341β342. MR**258044**, DOI 10.1112/blms/1.3.341
R. C. Kirby, - John Milnor,
*On spaces having the homotopy type of a $\textrm {CW}$-complex*, Trans. Amer. Math. Soc.**90**(1959), 272β280. MR**100267**, DOI 10.1090/S0002-9947-1959-0100267-4 - L. C. Siebenmann,
*Approximating cellular maps by homeomorphisms*, Topology**11**(1972), 271β294. MR**295365**, DOI 10.1016/0040-9383(72)90014-6
β, - Norman Steenrod,
*The Topology of Fibre Bundles*, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR**0039258**
D. P. Sullivan, - C. T. C. Wall,
*Surgery on compact manifolds*, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR**0431216**

*Hurewicz fiberings of ANR*βs (preprint).

*Local homotopy properties of maps and approximation of fibre bundle projections*, Thesis, University of Georgia, 1976.

*Lectures on triangulation of manifolds*, Notes, UCLA, 1969. R. C. Kirby and L. C. Siebenmann,

*Foundations of topology*, Notices Amer. Math. Soc.

**16**(1969), 848. George Kozlowski,

*Variants of homotopy equivalence*, contributed lecture, CBMS/NSF Regional Conference on the theory of infinite dimensional manifolds and its applications to topology, October 11-15, 1975, Guilford College, Greensboro, N. C.

*The obstruction to finding a boundary for an open manifold of dimension greater than five*, Thesis, Princeton University, 1965.

*Triangulating homotopy equivalences*, Thesis, Princeton University, 1966.

## Additional Information

- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**258**(1980), 87-97 - MSC: Primary 57N99; Secondary 55R65
- DOI: https://doi.org/10.1090/S0002-9947-1980-0554320-2
- MathSciNet review: 554320