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Transactions of the American Mathematical Society

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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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