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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Taming and the Poincaré conjecture


Author: T. L. Thickstun
Journal: Trans. Amer. Math. Soc. 238 (1978), 385-396
MSC: Primary 57A10; Secondary 55A40, 57C30
MathSciNet review: 0482769
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0482769-6
PII: S 0002-9947(1978)0482769-6
Keywords: Suspension, taming, Poincaré conjecture, homology sphere, Heegaard splitting
Article copyright: © Copyright 1978 American Mathematical Society



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