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

Author:
R. E. Goad

Journal:
Trans. Amer. Math. Soc. **258** (1980), 87-97

MSC:
Primary 57N99; Secondary 55R65

MathSciNet review:
554320

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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.

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DOI:
https://doi.org/10.1090/S0002-9947-1980-0554320-2

Article copyright:
© Copyright 1980
American Mathematical Society