Taming and the Poincaré conjecture

Thickstun, T. L.

doi:10.1090/S0002-9947-1978-0482769-6

Taming and the Poincaré conjecture
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by T. L. Thickstun PDF

Trans. Amer. Math. Soc. 238 (1978), 385-396 Request permission

Abstract:

L. Glaser and L. Siebenmann have shown that the double suspension of a homotopy 3-sphere is homeomorphic to the 5-sphere. This result, together with a well-known characterization of ${S^3}$ due to R. H. Bing, is used to establish a relationship between the Poincaré conjecture and two conjectures concerned with taming embeddings in higher dimensions. One of the two conjectures, each of which implies the Poincaré conjecture, states, in effect, that a codimension two sphere is tame if it is tame “modulo” a tame disk contained in it.

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Geschlossen Flächen in drei dimensionalen Mannigfaltigkeiten

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