%0 Journal Article
%A Montesinos Amilibia, José María
%T The knot engulfing property of 3-manifolds.
%D 2010
%@ 1825-1269
%U https://hdl.handle.net/20.500.14352/43851
%X The Freudenthal compactification of a 3-manifold M is a compactification M′ such that the end space e(M)=M′∖M is a totally disconnected compact set. The topological uniformization conjecture states that the Freudenthal compactification of the universal covering of a connected, closed 3-manifold is S3 with its end space tamely embedded. A 3-manifold M has the knot engulfing property if every contractible polyhedral simple closed curve in M lies in some polyhedral 3-cell in M. A classical result by Bing (1958) is that the only simply connected closed 3-manifold with the knot engulfing property is S3. The author proves a generalization of Bing's result: A simply connected 3-manifold M has the knot engulfing property if and only if the Freudenthal compactification M′ of M is homeomorphic to S3 with the end space e(M) tamely embedded.    Thus the topological uniformization conjecture can be rephrased as stating that the universal covering of a connected, closed 3-manifold has the knot engulfing property.
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