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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57A10, 55A40, 57C30

Retrieve articles in all journals with MSC: 57A10, 55A40, 57C30

Additional Information

Keywords: Suspension, taming, Poincaré conjecture, homology sphere, Heegaard splitting
Article copyright: © Copyright 1978 American Mathematical Society