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

Goad, R. E.

doi:10.1090/S0002-9947-1980-0554320-2

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.

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